Question

The population of your hometown can be modeled by the equation P equals 2538 left parenthesis 1.025 right parenthesis to the power of t where t represents the number of years since 2000. What was the population of your hometown in 2000? By what percent did the population increase each year?

Answer 1

2538

2.5%

Explanation:

The population equayio since year 2000 can be modeled mathematically as :

P = 2538(1.025)^t

This is an exponential growth function which is represented by the general formula :

y = a(b)^t

Where, a is the initial population ;

b = growth factor ; b = (1 + r) where r = growth rate

Comparing the equations, the population in year 2000 represents the initial population, a = 2538

The percentage Rate of increase in population is :

(1 + r) = 1.025

r = 1.025 - 1

r = 0.025 ; 0.025 * 100% = 2.5%