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Financial Polynomials
Financial Polynomials
Name of Student:
MATT 221
Professor’s Name:
Date:
Financial Polynomials
Polynomials are expressions that involve more than two algebraic terms especially sum of various terms which contain different powers but of the same variable. The word comes from ‘poly-‘meaning many and ‘nomial’ meaning terms. Financial polynomials are expressions that are used to calculate the present or values of funds. They are mostly used by people who engage in fund management for example in banks and insurance firms. Its importance can never be overestimated.
‘‘P dollars is invested at annual interest rate r for I year. If the interest is compounded semiannually, then the polynomial P (1 + r/2)2 represents the value of the investment after I year. Rewrite this expression without parentheses. Evaluate the polynomial if P: $200 and r – l0%-’’ (Dugopolski, 2012). The instruction is that the expression is to be rewritten without parenthesis. This means FOIL and then multiplies all the terms by P.
P (1 + r/2)2 this is the original expression with the exponent
P (1 + r/2) (1 + r/2)the squared quantity the multiplies itself
P (1 + r/2 + r/2 + r2/4) the result due to carrying out FOIL
P (1 + 2r/2 + r2/4)like terms are combined that is r/2 + r/2 = 2r/2
P + 2Pr/2 + Pr2/4the P is distributed across the trinomial
The polynomial is not in descending order as it has the highest exponent in the last term instead of the first term so it is in an ascending order. This is an expression and not an equation so a solution for the variables cannot be found unless given values to use.
Then the polynomial formula with two different sets of numerical information will be solved. In these types of problems, a single numeric value will be found that represents the total.
1. P = $200 and r = 10% = 10 r given as a decimal instead of a percent
P + 2Pr/2 + Pr2/4 the expanded formula
200 + 2(200) (0.10)/4 + 200(0.10)2/4 values are substituted into the formula
200 + 400(0.10) /4+ 200(0.01) /4 exponents and Multiplication
200 + 10 + 0.5 Finish order of operations with addition
210.5 The final result of the formula
Therefore $200 left alone for a year at 11% compounded annually results in $210.50 according to the formula.
The second set of numerical information gives us the following working:
P = $6780 and r = 2.5% = .025 Interest rate as a decimal number
P + 2Pr/4 + Pr2/4the expanded formula
6780 + 2(6780) (.025)/4 + 6780(.025)2/4 values substituted in
6780 + 84.75 + 1.059375 Order of operations and decimal rules used.
6865.8094 The final result of the formula
Starting with $6780 and compounding 2.5% interest once a year yields $85.8094 in interest at the end of one year for a total of $6865.8094.
The final part of the assignment involves simplifying a polynomial expression. To do this, like terms, distributive property, and order of operations must be used
(-9×3 + 3×2 – 15x) ÷ (-3x)the original expression
(-9×3 + 3×2 – 15x) rewrite the equation for clarity
-3x
-9×3 + 3×2 – 15xdivide each term by the denominator
-3x -3x -3x
3×2 + x + 5 the final answer
In summary, the application of financial polynomials has helped calculate the future values of funds given the interest rates. Given the principal and the interest rates, one is able to determine the future value of the fund depending on the time frame given for the investment using the formula P (1 + r)2 . The polynomials ensure that there is accuracy when making these calculations. Bankers, insurers, mortgage institutions among others will always need financial polynomials to succeed in their fields.
Reference
Dugopolski, M. (2012). Elementary and intermediate algebra (4th Ed.). New York, NY: McGraw-Hill Publishing.
Krause, E. F. (2012). Taxicab geometry: An adventure in non-Euclidean geometry. Courier Dover Publications.
Irreversible Effect of Global Warming
Irreversible Effect of Global Warming Name
Institution
Year
The debate amount climate change and its effect on the humans, would animals, and plants has been raging for years. The neglect and abuse of the serene environment due to increased exploitation of natural resources has caused the climate to go beyond points of zero recovery. Today, millions of people living along coastal areas are already losing their habitat due to risking seas and this spells danger to the world. Climate change and global warming is said to be irreversible because it has gone beyond the tipping point. A study published in 2009, led by a scientist with the National Oceanic and Atmospheric Administration, shows that climate change may in fact be irreversible. Still, the value and impact of the climate change can be seen far beyond where the damage is occurring and this includes things like bad weather, extreme heat, rainfall and flooding. The economic cost of global warming is said to amount to billions of dollars annually with the figures expected to rise even higher.
Global warming can only reverse if it is within limited reaches. However, the current global warming fates only shows that the world is to a point where it cannot reverse the situation. The world is today experiencing temperatures at rates that have never been recorded before (Hughes et al., 2017). The issue has even gotten worse in areas where some of the climate experts are waring of even higher temperature rise. Students have shown that in the current rates, the climate change may even become uncontrollable. The major issue in this regard is that the burning of fossil fuels is only adding fuel to the fire that is making the issue of global warming even more dangerous (Hanna & Tait, 2015). There is a lot of concern among climate experts that the current rates of fossil fuel burning will create trajectory that may be hard to reverse.
The other reason that makes global warming irreversible is that the climate safety commitments are being ignored and broken that makes the issue worse. For example, the U.S. pulling out of the 2015 Paris climate Accord under the Trump’s administration was heavily criticized by global leaders. Such actions that go contrary to the efforts being laid down in securing the world only point to the dangers that lie ahead in regard to the global warming. Still, the commitment to other climate safety laws mainly regarding coal burning has been ignored by counties like China thus adding to the risk of worse global warming in the future (McGlade & Ekins, 2015). Perhaps the issue can only be addressed when the world comes together and admits that human kind will exterminate itself through ignorance of the matter. Even with the adequate efforts being put, the issue of global warming still poses great risk to the stability in climate.
With the current state of lobal warming, expert have argued that the world still has chance to make things better. The safety of the world climate leis in the collective responsiveness to the dangers that lie ahead where every country has to play its part (Hughes et al., 2017). More compelling is the observed neglect of the global laws meant to restrict abuse of the resources like coal and other fossil fuels. There is an unfriendly competition in the global economy that is having great repercussions on the climate as the country go beyond the norms to attain the needed growth. Despite the fact that global warming currently appears irreversible, there is hope on what can be done to reduce the speed at which things are worsening (Hanna & Tait, 2015). The first approach to slow things down relates to the individua action and concern that every country has to take.
The global warming issue is already out of hand and more problems are projected to occur in the future. One of the things that makes the global warming issue appear irreversible is the continued ignorance and neglect of the laid down laws that are meant to curtail abuse of the climate (Hughes et al., 2017). For example, some countries are already going contrary to the 2015 Paris Climate Accord that has been a fundamental cause of the deteriorating issue of global warming. More efforts being out to deal with global warming have already proven weak. For example, the shift to electric cars is yet to show any significant in the area of fossil fuel burning. Another outlook into this is the neglect of the basic guidelines that have been out in the area of climate control. Still, global warming is being contributed by deforestation that has over the past ten years occurred at unprecedented rates. The burning of large forests like Amazon has raised concerns over the safety of the climate as more trees are being brought down (Feller, 2016). Global warming thus stands at irreversible state with more threats being out across the world. The loss of the basic pillars of climate regulation like the forests and the vast use of fossil fuels has led to the pressure on the climate.
Increased population across the globe is said to be the main cause of the global warming as the exploitation of resources continue to rise (Hughes et al., 2017). More and reclamation has led to the cutting down of trees and destruction of other natural habitats. These actions are collectively adding to the danger of climate change that has also led to massive loss of basic climate protective elements. More so, the adverse needs to meet the global demand for fossil fuel and the economic growth appetite has made many governments overlook the dangers lie ahead. The world is consuming resources at a fast rate than ever before and this is having effects on the climate (Hanna & Tait, 2015). The case of fossil fuels burning only points to some of the issues that needs to be addressed. With the situation projected to get worse, the issue of global warming will only intensify and thus put more pressure on the climate stability. More efforts need to be laid down particularly on the area of neglect of the current laws that are meant to safeguard the climate (McGlade & Ekins, 2015).
Conclusion
Global warming is already a major issue of this age that is affecting people at the furthest reaches of the globe. Solutions to the issue appears far from reach due to the ignorance from the governments and individuals. For now, global warming remains irreversible due to the deteriorating cases of abuse of the global resources that is putting pressure on the climate. The major concern over the irreversible state of the global warming is that most countries are still ignorant over the dangers ahead. The developed counties have been cautioned over their actions that are even putting the world in greater danger. Rising temperatures and worsening weather will likely get worse with time as the issue of global warming intensifies.
References
Feller, U. (2016). Drought stress and carbon assimilation in a warming climate: Reversible and irreversible impacts. Journal of Plant Physiology, 203, 84-94.
Hanna, E. G., & Tait, P. W. (2015). Limitations to thermoregulation and acclimatization challenge human adaptation to global warming. International journal of environmental research and public health, 12(7), 8034-8074.
Hughes, T. P., Kerry, J. T., Álvarez-Noriega, M., Álvarez-Romero, J. G., Anderson, K. D., Baird, A. H., … & Bridge, T. C. (2017). Global warming and recurrent mass bleaching of corals. Nature, 543(7645), 373-377.
McGlade, C., & Ekins, P. (2015). The geographical distribution of fossil fuels unused when limiting global warming to 2 C. Nature, 517(7533), 187-190.
In October 2018, one person won a Mega Millions jackpot worth 1.54 billion dollars. How would you express that jackpot amount
1. In October 2018, one person won a Mega Millions jackpot worth 1.54 billion dollars. How would you express that jackpot amount in scientific notation?
1.54 × 1061.54 × 10915.4 × 10615.4 × 1092. In Major League Baseball, fans eat approximately 21 million hot dogs every season. There are a total of 2,430 games in each season. Approximately how many hot dogs are eaten at each game?
1,000 hot dogs
9,000 hot dogs
90,000 hot dogs
1 million hot dogs
The United States has two bodies of Congress: the Senate and the House of Representatives. There are 435 seats in the House of Representatives. On November 9, 2018, following elections, 226 seats belonged to members of the Democratic party and 198 seats belonged to members of the Republican party. Election results were still undecided for the other 11 seats.
Republicans were leading 7 of the undecided races and Democrats were leading 4. If the 7 leading Republicans and 4 leading Democrats won their races, what percent of the seats in House of Representatives would belong to Democrats and what percent would belong to Republicans? Round answers to the nearest percent.
Democrats would hold 46% of the seats and Republicans would hold 52% of the seats.
Democrats would hold 50% of the seats and Republicans would hold 50% of the seats.
Democrats would hold 52% of the seats and Republicans would hold 46% of the seats.
Democrats would hold 53% of the seats and Republicans would hold 47% of the seats.
4. A syllabus in a student’s mathematics course states that she can earn 450 points on homework, 100 points on attendance, and 800 points on exams. What percent of her final grade is determined by her attendance? Round to the nearest percent.
7%
10%
13%
74%
5. Smoking-related illness in the United States costs more than $300 billion each year. In 2017, the gross domestic product (GDP) of the United States was $19.39 trillion. Calculate the total economic impact of smoking (cost) as a percentage of the United States’ GDP. Round your answer to the nearest hundredth of a percent.
0.02%
0.15%
0.65%
1.55%
6. Two students went shopping and bought $150 worth of clothes. They had to pay an additional $14.78 in tax. Estimate the tax rate they had to pay.
About 5%
About 10%
About 14%
About 15%
7. George took his long-time crush on their first date. They went to dinner where he spent $84.50 and left an additional 20% tip. Later he paid for two movie tickets that cost $12.50 each and bought snacks at the movie that cost a total of $14.45. Which equation would calculate how much George spent on his date?
84.50 + (0.20 x 84.50) + (2 * 12.50) + 14.45
1.20 x 84.50 + 12.50 + 14.45
1.20 (84.50 + 12.50 + 14.45)
84.50 + (1.20 x 84.50) + 12.50 + 12.50 + 14.45
8. In 2018, a Quinnipiac University poll found that 65% of Florida voters support stricter gun laws. There are approximately 13 million registered voters in Florida. If the poll represents how all voters in Florida feel, which of the following is the best estimate of the number of voters who support stricter gun laws?
Between 130 thousand and 650 thousand voters
Between 1.3 million and 2.3 thousand voters
Between 4 million and 5 million voters
Between 8 million and 9 million voters
Use the following information to answer the next two questions.
9. A high school student is writing a report on which social media site, Facebook or Instagram, is preferred by Millennials (people born between 1980 and 1994) compared to Generation Z (people born 1995 or later). The results of her survey are below.
Facebook InstagramTotal
Millennials530 504 1034
Generation Z 129 905 1034
Total 659 1409 2068
Which of the following conclusions could be accurately drawn from these results?
Approximately 25% of Millennials surveyed prefer Facebook
Approximately 36% of Millennials surveyed prefer InstagramApproximately 50% of Generation Z surveyed prefer Facebook
Approximately 90% of Generation Z surveyed prefer Instagram10. The student made the calculation shown below. What question was she trying to answer?
504 ÷ 1409
What percentage of those who prefer Instagram are Millennials?
What percentage of those who prefer Facebook are Millennials?
What percentage of Millennials prefer Instagram?
What percentage of Millennials prefer Facebook?
11. A 2018 Chevrolet Suburban averages 15 miles per gallon of gas in the city. It drives 47% farther per gallon of gas on the highway. If gas costs $3.25 per gallon, how much does a Suburban cost to drive per mile on the highway? Round to the nearest cent
7 cents per mile on the highway
15 cents per mile on the highway
22 cents per mile on the highway
153 cents per mile on the highway
12. The following data table gives information about the change in smartphone sales of two leading companies from 2007 to 2017.
Company Smartphones sold in 2007 Smartphones sold in 2017 Smartphones sold in 2027
Apple 2.3 million 214.9 million ?
Samsung 435.5 million 321.3 million ?
The number of smartphones sold is changing for these companies every year. Suppose that over the next 10 years, from 2017 to 2027, their absolute rates of change of smartphone sales remains the same as the previous 10 years. Using the data table, determine which of the following statements would be true.
Samsung will sell more smartphones that Apple in 2027.
Samsung will sell over 400 million smartphones in 2027.
Apple will sell over 400 million smartphones in 2027.
Apple and Samsung will sell approximately the same number of smartphones in 2027.
Date 3/1/98 1/1/01 1/1/02 1/1/07 1/1/08 7/1/14 1/1/16 1/1/17 1/1/18
Minimum Wage $5.75 $6.25 $6.75 $7.50 $8.00 $9.00 $10.00 $10.50 $11.00
13. California’s minimum wage (in dollars per hour) has increased substantially over the last 20 years, as seen in the table below.
Which of these graphic displays should be used to show the rate of change, or trend, of these minimum wage rates over time?
a. A bar graphb. A line graphc. A pie chart
d. A table displaying the mean and median
15. The table below shows the yearly income of a random sample of family physicians across the US in 2018.
Doctor Income in 2018
Dr. Bonner$108,000
Dr. Dupree$210,000
Dr. Gilbreath$145,000
Dr. Griner$190,000
Dr. Hornbuckle$135,000
Dr. Houston$180,000
Dr. Kizer$187,000
Dr. Taurasi$162,000
Dr. Taylor$151,000
Dr. Thomas$235,000
Calculate the mean and median income in 2018 for these doctors.
Mean = $162,000, median = $171,000
Mean = $167,800, median = $162,000
Mean = $170,300, median = $171,000
Mean = $171,000, median = $180,000
Use the following information to answer the next two questions.
19. The cost of Carlos’s electric bill (E) is computed by using a monthly charge of $29.99 plus $0.11 per kilowatt hour (k), as follows:
E = 0.11k + 29.99
Solve this equation for k.
E0.11 – 29.99 = k
E0.11 + 29.99 = k
(E – 29.99) / 0.11 = k
(E + 29.99) / 0.11 = k
Use the following information to answer the next two questions.
22. Which of the following could be a model for the amount of money (A) Maddie’s saving account will contain after (w) weeks?
A = 300w
A = 300 + 0.03w
A = 300 + 1.03w
A = 300 * 1.03w
23. A 21-year-old in New York wants to figure out how much he will spend at a new club, Club C. He figures out that his cost can be calculated using the formula below. Which of the following could be an interpretation of this formula?
C = 20 + 12D
The cost he will pay to go to Club C is a $12 cover charge plus $20 per drink.
The cost he will pay to go to Club C is a $20 cover charge plus $12 per drink.
The cost he will pay to go to Club C is $20 after 12 AM.
The cost he and his friends will pay to go to Club C is a $32 per person.
25. The average price of 42-inch TVs has gone down dramatically over the past 20 years. The graph below shows the approximate average price of a 42-inch TV each year, beginning in 1998. The equation to model this is:
P = $1200 * .97 t
Where:
P = the average price of a 42-inch TV
t = number of years since 1998
Which of the following statements gives the best interpretation of this model?
The average price of a 42-inch TV has decreased by $97 every year
The average price of a 42-inch TV has decreased by $36 each year
The average price of a 42-inch TV has decreased by 3% every year
The average price of a 42-inch TV has decreased by 97% every year
26. Recall that the formula for earnings on a principal investment compounded annually is:
A = P * (1 + r)tWhere:
A = amount in the fund
P = principal (initial amount invested)
r = Annual Percentage Rate (APR) (as a decimal)
t = time in years, or term
If you invest $3,000 into each of the four options below, which option would yield the highest amount at the end of the term?
12 years, 3% APR
8 years, 5% APR
6 years, 7% APR
4 years, 10% APR
27. Nikolas invests $1,400 into a certificate of deposit that earns 1.8% compounded semiannually (twice a year). How much money will he have at the end of 5 years? Use the compound interest formula given below. Round final answer to the nearest cent.
A = P(1 + r/n)n*t
Where:
A = the amount in the account
P = the original principal
r = the annual interest rate
n = the number of compounding periods in a year
t = the number of years
$1,530.62
$1,531.23
$1,673.42
$3,314.31
Part 2: Open Ended Items
For Part 2: Write your work and answers on the test. The answer sheet is not needed for this section.
An Amazon Echo originally costs $99.99. It is on sale for 10% off. Sales tax of 7.5% is then added to the sale price. What is the cost of the Echo on sale including tax? Round your answer to the nearest penny.
The population of Minnesota is about 5.577 million people. Write Minnesota’s population in standard notation (as a number).
In 2018, the Unites States had a population of 325.7 million people. Of these, 11.66 million lived in Ohio. What percent of all people in the United States lived in Ohio in 2018? Round your answer to the nearest tenth of a percent.
As people are living longer and the world’s population is increasing, there are more and more people ages 65 or older. In 2000, approximately 419 million people were 65 or older. By 2017, that number increased to 656 million. On the two questions below, round to the nearest tenth when relevant.
a. What was the absolute change in the number of people 65 or older from 2000 to 2017?
b. What was the relative change in the number of people 65 or older from 2000 to 2017?
A student downloaded a new game on her phone that was recommended by her friend. She wanted to show her friend how good she was doing, so she wrote down all her scores on the game. Her first five scores on the game were 432, 543, 348, 788, and 823. On the two questions below, round to the nearest whole number when relevant.
a. What is her mean, or average, score on the game?
b. What is her median score on the game?
Using the equation:
d = r * t
Where:
d = distance traveled
r = rate (speed, velocity)
t = time
If you have to fly from JFK airport in New York to LAX airport in Los Angeles, you will fly 2,475 miles. If the average amount of time for a plane to fly from JFK to LAX is 5 hours and 30 minutes, what is the average speed that a plane flies on this trip? Include the appropriate units.
You need to buy bananas at the store, but you realize you only have $2. How many bananas could you buy if they each cost 30 cents? (Hint: you cannot buy a fraction of a banana).
After trick-or-treating, a boy opened all of his M&Ms and put them into one big jar. He ate the same amount of M&Ms each day until they were gone. He made a graph, shown below, to represent how many M&Ms he had left over time. His teacher explained that his situation could be modeled by a linear equation where M represents the amount of M&Ms left and d represents the number of days since Halloween that had passed. Use the student’s graph to answer the following questions.
a. Circle the horizontal intercept on the graph.
b. What information does the horizontal intercept tell you, in the context of this problem?
c. What is the slope of the line on the graph?
d. What information does the slope tell you, in the context of this problem?