Answer:
[tex]\boxed{11 576}[/tex]
Explanation:
Your first problem is to figure out the formula to use.
You have an initial population P₀ = 10 000.
The population P increases by 5 %, that is, by a factor of 1.05.
Each year, you multiply the population of the previous year by 1.05.
This gives you a geometric series, for which the general formula is
P = P₀rⁿ
P₀ = 10 000
r = 1.05, the common ratio from one year to the next
n = the number of years from now
The formula for your population is then
P = 10 000(1.05)ⁿ
If n = 3
P = 10 000(1.05)³ = 10 000 × 1.1576 = 11 576
[tex]\text{At the end of the third year the population of beetles will be $\boxed{\textbf{11 576}}$}[/tex]
