Question

The population of a county is growing at a rate of 9% per year, compounded continuously. If the county currently has 14,934 people, how many will there be in this county in 10 years? Round to the nearest person.

Answer 1

The population of the county in 10 years will be approximately 36,704.

Step-by-step explanation:

To calculate the population of the county in 10 years, we can use the formula for continuous compound interest, A=p
Where:
A = final population
P = initial population
r = growth rate
t = time in years
e = Euler's number (approximately 2.71828)

Substituting the given values into the formula:
A = 14,934 * e^(0.09 * 10)
A ≈ 14,934 * e^0.9
A ≈ 14,934 * 2.4596
A ≈ 36,703.7

Rounding to the nearest person, the population of the county in 10 years will be approximately 3670