Question

The exponential growth model y = Ae^rt can be used to calculate the future population of a city. In this model, A is the current population, r is the rate of growth, and y is the future population for a specific time, t, in years.

A certain city's population has a growth rate of r = 0.08. Approximately how long will it take the city's population to grow from 250,000 to 675,000?

NEED ASAP

Answer 1

To determine the time it takes for the city's population to grow from 250,000 to 675,000, we can use the exponential growth model formula:

y = Ae^(rt)

In this case, the initial population (A) is 250,000, and the future population (y) is 675,000. The growth rate (r) is given as 0.08. We need to solve for time (t).

675,000 = 250,000 * e^(0.08t)

To solve for t, we can take the natural logarithm (ln) of both sides:

ln(675,000) = ln(250,000 * e^(0.08t))

ln(675,000) = ln(250,000) + ln(e^(0.08t))

ln(675,000) = ln(250,000) + 0.08t

Now, we can isolate t by subtracting ln(250,000) and dividing by 0.08:

0.08t = ln(675,000) - ln(250,000)

t = (ln(675,000) - ln(250,000)) / 0.08

Calculating this value will give us the approximate time it takes for the population to grow from 250,000 to 675,000.

Answer 2

Explanation:

in the formula

y = Ae^rt

y is 675,000

A is 250,000

r is 0.08

to get the value of t

y = Ae^rt

y/A = e^rt

ln(y/A) = rt

[ln(y/A)]/r = t