Question

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?

Answer 1

Answer:

a. y = 4,200 $0.976^{4t}$

b. 9.2%

Step-by-step explanation:

Given the information:

• The intinital value: 4,200

• The population is decreasing at a rate of 2.4% per year

=> 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 $0.976^{4t}$

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

Let t = 0 we have: y(0) = 4,200 $0.976^{4*0} = 4200$

Let t = 1 we have:  y(1) = 4,200 $0.976^{4*1} = 3811$

=> the decreasing percentage is:

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

= (4200 - 3811) / 4200 *100%

= 389/4200*100%

= 9.2%