Question

Which equation relates the population (P) in millions to the time that has passed (T) if the growth rate is 4% per year and the starting

population is 10 million people?
(1) P = 10(0.96)^T
(2) P = 10(1.04)^T
(3) P = 10 + 10(0.04)^T
(4) P = 10(1.4)^T

Answer 1

Explanation:

The model for exponential growth/decay is

`P(t)=a(b)^t` where a is the initial population and b is the growth/decay rate. Filling in the info you were given:

`P(t)=10(1.04)^t`

Because this is a growth rate, we have 100% of the population and that population is growing by 4%, which is .04 in decimal form. If the population is not declining, we are adding to the 100% of the population we already have. That's why the growth rate is 1.04.

.96 means that the population is declining at 4% each year; and 1.4 means that the population is growing at 140% instead of the 104% that it is.