Question

The rabbit population in a forest area grows at the rate of 6% monthly. if there are currently 260 rabbits, find how many rabbits (rounded to the nearest whole number) should be expected twelve months from now? (assume continuous compounding exponential growth).

Answer 1

For this case we have a function of the form:

$y = A * (b) ^ x$

Where,

A: initial population of rabbits

b: growth rate

x: time in months

Substituting values we have:

$y = 260 * (1.06) ^ x$

For the month number 12 we have:

$y = 260 * (1.06) ^ {12}y = 523,171$

Rounding to the nearest whole number we have:

$y = 523$

Answer:

For month number 12, the approximate population of rabbits is:

$y = 523$