U4.L1.HW: Exponential Functions: Question 24

Question

Explain your answer afterwards.

A population numbers 17,000 organisms initially and decreases by 7% each year.

Suppose  represents population, and  the number of years of growth. An exponential model for the population can be written in the form P = ab^t, where

P = ___________

Answer 1

P = ab^t

a is the initial value (17,000) ; b is the effective annual rate of increase or decrease; t is the number of years in this case.

If something neither increases or decreases it remains at 100% of the initial value. However, if it decreases at 7% each year, then the rate becomes 100% - 7%, or 93%

The formula here is P = 17,000(1 - 0.07)^t or P = 17,000(0.93)^t

Note that the rate is expressed in decimal form.