Question

The current student population of Memphis is 1600. If the population decreases at a rate of 13.9% each year. What will the student population be in 7 years?Write an exponential growth model for the future population P(x) where x is in years:P(x)=What will the population be in 7 years? (Round to nearest student)

Answer 1

Step-by-step explanation:

The formula for calculating exponential growth is expressed as

P(x) = Po(1 + r)^x

where

A is the final amount after time t

Po is the initial amount

r is the growth rate

x is the time

In this case, the population is decreasing. The formula would be

P(x) = Po(1 - r)^x

From the information given,

Po = 1600

r = 13.9% = 13.9/100 = 0.139

Thus, the exponential decay model is

P(x) = 1600(1 - 0.139)^x

A = 1600(0.861)^x

In 7 years, the population would be

P(7) = 1600(0.861)^7

P(7) = 561

In 7 years, there would be 561 students