https://file.aiquickdraw.com/mathbot/file/1728301182740zsosp9k4.jpg

This is a compound interest-like problem where the area covered by the fire increases by 17% each hour. Given the current area of 32 m², we need to calculate how much area it will cover after 20 hours, assuming the fire spreads at the same rate.

We can use the formula for compound growth:

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

Where:
- \(A\) is the final area after \(t\) hours.
- \(P = 32 \, \text{m}^2\) is the initial area.
- \(r = 0.17\) (17% growth rate per hour).
- \(t = 20\) hours.

Substituting the values:

\[
A = 32 \times (1 + 0.17)^{20}
\]
\[
A = 32 \times (1.17)^{20}
\]

Now, calculating \(A\):

\[
A \approx 32 \times 23.609
\]
\[
A \approx 755.49 \, \text{m}^2
\]

Rounding to the nearest whole number, the area will be approximately **755 m²** in 20 hours.

Would you like more details, or do you have any questions?

Here are some related questions for further practice:
1. What would the area be if the fire spread for 15 hours instead of 20?
2. If the fire spreads for 25 hours, what area will it cover?
3. How would the formula change if the growth rate were 20% instead of 17%?
4. What if the initial area were 50 m² instead of 32 m²—how would that affect the area after 20 hours?
5. How long would it take for the fire to cover 1000 m² at this growth rate?

**Tip:** When solving compound growth problems, always ensure the rate is expressed as a decimal (e.g., 17% becomes 0.17).

The area covered by a fire increases by 17% each hour. Currently, the fire covers an area of 32 m². If the fire continues to spread at the same rate, what area will it cover in 20 hours’ time? Give your answer to the nearest 1 m².

Solve an exponential growth problem where a fire spreads at a rate of 17% per hour. Find the area covered after 20 hours, starting from an initial area of 32 m². The solution uses exponential growth formulas and is suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation