Please help with math

Question

A species of extremely rare, deep water fish rarely have children. If there are a 821 of this type of fish and their growth rate is 2% each month, how many will there be in half of a year, in 2 years, and in 10 years? Define a function and show work.

Answer 1

This is an example of exponential growth. At the end of each month, you will have 1.02 times the number you had at the start of the month.

p(n) = p₀ (1.02)ⁿ

p₀ = initial population = 821

n = number of months elapsed from when the population was 821

p(n) = 821 (1.02)ⁿ

Plug into the equation the number of months (n) in half a year, 2 years, and 10 years, and evaluate.