Question: 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? Give your answer to the nearest 1 m².
1. **State the problem:** We want to find the area covered by the fire after 20 hours, given it increases by 17% each hour and currently covers 32 m².
2. **Formula used:** The area grows exponentially, so we use the compound growth formula:
$$ A = A_0 \times (1 + r)^t $$
where:
- $A$ is the area after $t$ hours,
- $A_0 = 32$ m² is the initial area,
- $r = 0.17$ is the growth rate per hour,
- $t = 20$ hours is the time.
3. **Calculate the growth factor:**
$$ 1 + r = 1 + 0.17 = 1.17 $$
4. **Calculate the area after 20 hours:**
$$ A = 32 \times 1.17^{20} $$
5. **Evaluate the exponent:**
$$ 1.17^{20} \approx 22.939 $$
6. **Multiply by initial area:**
$$ A = 32 \times 22.939 = 734.048 $$
7. **Round to nearest 1 m²:**
$$ A \approx 734 \text{ m}^2 $$
**Final answer:** The fire will cover approximately 734 m² after 20 hours.