A a population shrinks from its initial level of 27,000 at a continuous decay rate of 6.9% per year By what percent does the population shrink each year?

Answer 1

P(t) = 27000e^-0.065t = 27000·(e^-0.069)^t = 27000·0.9333^t

^{So, each year population decreasing by 100% - 93.33% = 6.667%}

Answer 2

Hello Jackson,

The equation that describes this population decay is: P(t) = 27000 e^-0.069t. We used e here b/c you're told it's a continuous decay.

Now, let's rewrite this equation so it looks like a*b^t : P(t) = 27000 (e^-0.069)^t

Check out how now, the initial population a = 27000 and your base b = e^-0.069

The base is the growth/decay factor, and you're asked to find the percentage by which the population shrinks each year. In other words, you're asked to find the decay rate.

To find the growth/decay rate, you wanna do:

growth/decay rate = (growth factor - 1) * 100%

so: (e^-0.069 - 1)*100 = (0.9333 - 1) *100 = -0.06667*100 = -6.67% ---> negative percentage means decay

So the population shrinks each year by 6.67%