Question: The area covered by a fire increases by 13% each hour. Currently, the fire covers an area of 58 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 13% each hour and currently covers 58 m².
2. **Formula used:** This is an exponential growth problem. The formula for exponential growth is:
$$ A = A_0 \times (1 + r)^t $$
where:
- $A$ is the amount after time $t$,
- $A_0$ is the initial amount,
- $r$ is the growth rate per time period (as a decimal),
- $t$ is the number of time periods.
3. **Identify values:**
- $A_0 = 58$ m²
- $r = 13\% = 0.13$
- $t = 20$ hours
4. **Calculate:**
$$ A = 58 \times (1 + 0.13)^{20} = 58 \times 1.13^{20} $$
5. **Evaluate $1.13^{20}$:**
Using a calculator, $1.13^{20} \approx 11.367$
6. **Multiply:**
$$ A = 58 \times 11.367 = 659.886 $$
7. **Round to nearest 1 m²:**
$$ A \approx 660 \text{ m}^2 $$
**Final answer:** The fire will cover approximately 660 m² after 20 hours.