the population of hartford county is 125,000 and growing at a rate of 8.3% per year.

Question

use a continuous change model to predict the population in 15 years if the population continuous to grow at the same rate.

Answer 1

We can simply use the formula for continuous growth. It comes in diferent forms but each variable means the same thing. We can use the formula A = Pe^rt.

A is our final value. In this case our population after 15 years

P is the principal amount, our starting point which is 125,000

r is our rate of change. This is usually in percent form. We have 8.3% which is 8.3/100 = 0.083

t is time. How often are we changing in a given time frame. We know t is 15.

e is a special number used for continuous growth. Don't worry about e for now. It is one of the numbers you learn about in higher level math.

Huzzah, this means we can just plug it in. We don't need to solve for any variable and can just use a calculator.

A = 125000e^0.083*15

A = 434,116.8499

Our population in 15 years will be 434,117 citizens rounded up.