A population numbers 11,000 organisms initially and decreases by 4.6% each year.

Question

A population numbers 11,000 organisms initially and decreases by 4.6% each year. Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P = a ⋅ b t where

P =

please give answer and explain

Answer 1

Hi Leon. I see you've placed a lot of problems on exponential growth and decay on the help board today. These all fit the same pattern:

P = a(b)^t where "a" is the initial amount (the amount when you click the stopwatch at t = 0) and "b" is the amount the either grow or shrink by. To find "b" you start with "1" and either add the decimal growth rate if it is increasing or subtract the decimal "shrinking rate" if it is decreasing. And then "t" is the amount of time that goes by.

So, in this case, the "a" value is 11,000 because that's the population at time zero. Because the population is decreasing, then "b = 1 - 0.046" or b = 0.954.

So the equation is P = 11000(0.954)^t