A population numbers 16000 organisms initially and decreases

A population numbers 16,000 organisms initially and decreases by 9.6% each year. Suppose P represents population, and t the number of years of decline. An exponential model for the population can be written in the form P = a . b where Use logs to determine the number of years until the population drops to 11,360 organisms. Round answer to 2 decimal places.

Solution

Intial amt = 160,00 ; growth = 9.6% per year

P = a.b^t

where a= 160,00 ; b= 1- 0.096 = 0.904

(A) P = 160,00( 0.904)^t

(B) P = 11360

So, 11360 = 16000(0.904)^t

Taking log of both sides:

0.71 = (0.904)^t

ln(0.71) = t*(ln(0.904))

t = 3.39 years