Question

The town of madison has a population of 25,000. The population is increasing by a factor of 1.12 each year. Write a function that gives the population P(t) in madison t years from now

Answer 1

The population P(t) at the end of year t is   $P(t) = 25,000 \times (1.12)^t$

Step-by-step explanation:

The initial population of town of Madison = 25,000

The rate at which the population is increasing = 1.12 times

So, the increase in population first year  :

( the initial population)  x $(1.12)^1$  = 1.12 x ( 25,000)  

= 28,000

So, the population at the end of first year = 28,000

Similarly, the increase in population second year  :

( the initial population)  x (1.12)²  =  ( 25,000)   x (1.12)²

= 31,360

So, the population at the end of second year =31,360

Now, to calculate the population in t years from now:

The population P(t) at the end of year t is

$P(t) = 25,000 \times (1.12)^t$