Question

Suppose a city with population 300 comma 000300,000 has been growing at a rate of 88​% per year. If this rate​ continues, find the population of this city in 1010 years.

Answer 1

To find the population of the city in 10 years given an annual growth rate of 88%, we can use the formula for exponential growth:

\[
P(t) = P_0 \times (1 + r)^t
\]

where:
- \(P(t)\) is the future population after time \(t\),
- \(P_0\) is the current population,
- \(r\) is the growth rate (as a decimal),
- \(t\) is the time in years.

Given:
- \(P_0 = 300,000\)
- \(r = 0.88\) (88% growth rate)
- \(t = 10\)

Substituting the values into the formula:

\[
P(10) = 300,000 \times (1 + 0.88)^{10}
\]
\[
P(10) = 300,000 \times (1.88)^{10}
\]

Next, we calculate \( (1.88)^{10} \):

\[
(1.88)^{10} \approx 12,045.65 \, (\text{using a calculator})
\]

Now, substitute this value back into the population formula:

\[
P(10) = 300,000 \times 12,045.65 \approx 3,613,695,000
\]

Thus, the projected population of the city in 10 years is approximately **3,613,695,000**.