Question

A city has a population of 672,000. The population y increases by 5% each year.

What will the population be after 5 years? Round your answer to the nearest whole person.

Answer 1

Sure!

To calculate the population of the city after 5 years, we need to use the formula for compound interest, which is:

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

Where:
A = the final amount
P = the initial amount (the population of the city)
r = the annual interest rate (5%)
n = the number of times the interest is compounded per year (since the population is increasing yearly, we assume n = 1)
t = the number of years (5)

So, plugging in the values we get:

A = 672,000(1 + 0.05/1)^(1*5)
A = 672,000(1.05)^5
A = 838,484.94

Rounding this to the nearest whole person gives us 838,485. Therefore, the population of the city after 5 years will be approximately 838,485.

Answer 2

Answer: about 494,314 people

Explanation:

P(t) = a(1+r)t

P(t) = total population (??)

a = initial population = 260,000

r = growth factor (the percent as a decimal) = 0.055

1 + r = 1 + 0.055 = 1.055

t = time in years = 12

So, we can substitute all our information and solve:

P(12) = 260,000(1.055)12 = 494,313.95

Rounding to the nearest whole person, 494,314 people in 12 years.