Question

A population of 120 beetles increases at an annual rate of 30%. How many beetles will there be in 16 years? Write an expression to represent the equivalent monthly population increase rate.

Answer 1

Answer:

Expression: $120(1.3)^{16}$

Beetles after 16 years: 7984 beetles

Step-by-step explanation:

Since the population increases 30% annually every year on the population size of that year, then we need to use a compound interest formula which would be the following

A = P (1 + r/n) (nt)

A = the future amount

P = the initial amount

r = the annual increase rate (decimal)

n = the number of times that interest/increase is compounded per unit t

t = the number of years

Using the values in the question the expression for this scenario would be the following

120(1 + (0.30 / 1))^(1*16)

$120(1.3)^{16}$

7984.99