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This problem involves exponential growth. To find the time it takes for a population to double, we can use the exponential growth formula:

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

where:
- \( A \) is the final population (double the initial population),
- \( P \) is the initial population,
- \( r \) is the growth rate (8% = 0.08),
- \( t \) is the time in years that we need to find.

Since we're looking for when the population doubles, \( A = 2P \). Substituting this into the equation, we get:

\[
2P = P \times (1 + 0.08)^t
\]

Dividing both sides by \( P \):

\[
2 = (1.08)^t
\]

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

\[
\ln(2) = t \times \ln(1.08)
\]

Now, solving for \( t \):

\[
t = \frac{\ln(2)}{\ln(1.08)}
\]

Let me calculate that.The time it will take for the city's population to double at a growth rate of 8% per year is approximately **9 years**.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:
1. How does the doubling time change if the growth rate increases to 10%?
2. How can you apply this formula to find out when a population triples?
3. What would the doubling time be if the growth rate were 5% instead of 8%?
4. Can this model be used for scenarios where the population decreases by a certain percentage per year?
5. How does exponential growth differ from linear growth?

**Tip:** Exponential growth can cause quantities to increase rapidly over time, especially with higher growth rates.

A city is growing by 8% per year. Find the time it takes for the population to double. Use yr for years.

Learn how to calculate the time it takes for a city's population to double with an 8% annual growth rate using exponential growth formulas and logarithms. Suitable for students in Grades 9-12.

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