Answer:
a. y = 4,200 [tex]0.976^{4t}[/tex]
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 [tex]0.976^{4t}[/tex]
b. The population is decreasing by how much percent per quarter?
Let t = 0 we have: y(0) = 4,200 [tex]0.976^{4*0} = 4200[/tex]
Let t = 1 we have: y(1) = 4,200 [tex]0.976^{4*1} = 3811[/tex]
=> the decreasing percentage is:
= (y(0) - y(1)) / y(0)*100%
= (4200 - 3811) / 4200 *100%
= 389/4200*100%
= 9.2%
