# Exponetial Growth and Decay

Exponential Growth and Decay

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Exponential Growth and Decay

Create a story problem that uses either exponential growth or exponential decay.

In 2009, there were 10000 smart phone users in the market.  The number of users has increased by 91% per year after to date.  How many smart phone users are in the market today?

This is an exponential growth and as such, the following formula applies:

y = a (1+r) x

where y = number of manual / hands

a = initial amount before measuring decay = 10000

r = decay rate (often a percent) = 91%

x = number of time intervals that have passed = 5

y then becomes

y = 10000 (1+0.91)5

y = 10000 (1.91)5

y = 10000 * 25.419

y = 250,000 because people cannot be considered in their fractions.

Problem to solve: Story Problem:  Due to enhancements in technology and automation, the manual hands on jobs at a firm which currently numbers 2500 is decreasing a rate of 20% per year.  What is the number of manual hands on jobs left after 3 years?

This is an exponential decay and as such, the following formula applies:

y = a (1-r) x

where y = number of manual / hands

a = initial amount before measuring decay = 2500

r = decay rate (often a percent) = 20%

x = number of time intervals that have passed = 3

y then becomes

y = 2500 (1-0.2)3

y = 2500 (0.8)3

y = 2500 * 0.512

y = 1280

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