type the correct answer in the box. use numerals instead of words. a population of beetles increases by 5%…

type the correct answer in the box. use numerals instead of words. a population of beetles increases by 5% every year. if at the start of the year the population is at 10,000 beetles, what will its population be after three years? at the end of the third year the population of beetles will be

type the correct answer in the box. use numerals instead of words. a population of beetles increases by 5% every year. if at the start of the year the population is at 10,000 beetles, what will its population be after three years? at the end of the third year the population of beetles will be

Answer

Answer:

11576.25

Explanation:

Step1: Identify the formula

The formula for compound - growth is $A = P(1 + r)^n$, where $P$ is the initial amount, $r$ is the growth rate as a decimal, and $n$ is the number of time periods.

Step2: Convert the percentage to a decimal

The growth rate $r=5% = 0.05$, $P = 10000$, and $n = 3$.

Step3: Substitute the values into the formula

$A=10000\times(1 + 0.05)^3$.

Step4: Calculate $(1 + 0.05)^3$

$(1 + 0.05)^3=1.05^3=1.05\times1.05\times1.05 = 1.157625$.

Step5: Calculate the final amount

$A = 10000\times1.157625=11576.25$.