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We are given that the fire area increases by 17% each hour, and the current area is 32 m². We need to find out what the area will be in 20 hours if the fire continues to spread at the same rate.

This is a problem involving exponential growth. The formula for exponential growth is:

\[
A(t) = A_0 \times (1 + r)^t
\]

Where:
- \( A(t) \) is the area after \( t \) hours.
- \( A_0 \) is the initial area (32 m²).
- \( r \) is the rate of growth per hour (17%, or 0.17).
- \( t \) is the time in hours (20 hours).

### Substituting the values:

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

Simplifying the equation:

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

We will calculate this step-by-step.

1. \( 1.17^{20} \approx 22.946 \)
2. \( A(20) = 32 \times 22.946 \)
3. \( A(20) \approx 734.272 \)

Rounding to the nearest square meter:

\[
A(20) \approx 734 \, m^2
\]

### Answer:
In 20 hours, the fire will cover approximately **734 m²**.

Would you like more details on any part of this solution, or do you have any further questions?

Here are five related questions you might find helpful:
1. How would the formula change if the growth rate varied each hour?
2. What if the fire spread by a fixed amount of area rather than a percentage?
3. How long would it take for the fire to reach an area of 1,000 m² at this rate?
4. What impact would doubling the growth rate have on the area after 20 hours?
5. Can this exponential growth model be applied to other real-life scenarios?

**Tip:** For exponential growth problems, always identify the base (1 + growth rate) and the exponent (time) to solve efficiently.

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?

Learn how to calculate the area covered by a fire that increases by 17% each hour. Starting with an initial area of 32 m², find out what the area will be after 20 hours using the exponential growth formula. Suitable for students in Grades 9-12.

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