If the initial population is 3800. Then the population of the cockroach after 3 years will be 1603.
Consider the function:
y = a(1 ± r)ⁿ
where n is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is a plus sign, then there is exponential growth happening by r fraction or r%.
If there is a minus sign, then there is exponential decay happening by r fraction or r%.
Colette has an exterminator visit regularly to control an ongoing cockroach problem.
It's been working, and the population has declined by 15% every year.
If the population is currently 3,800 cockroaches.
The expression is given as
y = 3800(0.75)ⁿ
Then the population of the cockroach after 3 years will be
y = 3800(0.75)³
y = 3800 x 0.4218
y = 1603.125
y ≅ 1603
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