the population of Knoxville is 500,000 and is increasing at the rate of 3.75% each year. Approximately when will the population reach 1 million?

when

500000(1.0375)^n = 1000000
or, less cumbersome,
1.0375^n = 2

To find out approximately when the population of Knoxville will reach 1 million, we need to calculate the number of years it would take for the population to increase from 500,000 to 1 million at a growth rate of 3.75% per year.

First, let's calculate how much the population increases each year. We can do this by multiplying the current population (500,000) by the growth rate (3.75%) expressed as a decimal (0.0375):

Population increase per year = 500,000 * 0.0375 = 18,750

Now, we can determine the number of years it would take for the population to double by dividing the difference between the target population (1,000,000) and the current population (500,000) by the annual population increase:

Number of years = (1,000,000 - 500,000) / 18,750

Number of years = 500,000 / 18,750

Number of years ≈ 26.67

Since we can't have a fraction of a year, we can round up the number of years to the nearest whole number. Therefore, it would take approximately 27 years for the population of Knoxville to reach 1 million.