Question

The population of a particular city is given by the function P(t) = 27,400(1.07)t, where t is the time in years and P(t) is the population after t years. What is the current population, the percentage growth rate, and the population size (rounded to the nearest whole person) after 5 years? Hint: Percentage Growth Rate = r ⋅ 100 in A = A0(1 + r)t

Answer 1

27,400 is the current population

7% is the rate of increase

The new size is:

• 38,430 is the population if t is an exponent

• 146,590 is t is NOT an exponent in the formula you typed

Explanation:

To find the population in a future year, use the formula:

`P(t) = 27,400(1.07)t`

Substitute the value t=5 to find the population in 5 years.

`P(t) = 27,400(1.07)t\\P(t) = 27,400(1.07)(5)\\P(t) = 146,590`

Or if the equation is supposed to have t as an exponent then look below:

`P(t) = 27,400(1.07)^t`

Substitute the value t=5 to find the population in 5 years.

`P(t) = 27,400(1.07)^t\\P(t) = 27,400(1.07)^(5)\\P(t) = 38,430`

This formula is based off the standard formula
`A=A_0(1+r)^t` so r, the rate is 1.07=1+0.07 so r is 7%.

`A_0` is the starting population which is 27,400 here.