Question

Explain

Initially, a population is 500, and it grows by 5% each year. Explain why the population is an exponential function of time.

Answer 1

Explanation:

the initial population is 500

after it grows 5% in 1 year we will have 500 * 1.05 ^1 because

500 represents 100% but

after 1 year we have 105% of the 500 people or 500*1.05 = 500 * 1.05 ^1

after 2 year we have 105% of 500*1.05 or 500*1.05*1.05 = 500 * 1.05 ^2

if we generalize

after x year we have 500 * 1.05 ^x

the population is an exponential function of time because the number of population depends on the number of years