In 1970, the population of a small town was 4,200. The population is decreasing at a rate of 2.4% per year. Which of the following shows an exponential decay function to find the quarterly decay rate?The population is decreasing by how much percent per quarter?

a. y = 4,200

b. 9.2%

Step-by-step explanation:

Given the information:

=> the base number of the exponential function is:

100% - 2.4% = 97.6% = 0.976

Let t is quarter

Let y is the population

=>  the following shows an exponential decay function to find the quarterly decay rate is:

y (t)= 4,200

b. The population is decreasing by how much percent per quarter?

Let t = 0 we have: y(0) = 4,200

Let t = 1 we have:  y(1) = 4,200

=> the decreasing percentage is:

= (y(0) - y(1)) / y(0)*100%

= (4200 - 3811) / 4200 *100%

= 389/4200*100%

= 9.2%

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