The area covered by a fire increases by each hour.
Currently, the fire covers an area of .
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 .

Ask by Collins Brooks. in the United Kingdom

Mar 30,2025

Question

The area covered by a fire increases by each hour.
Currently, the fire covers an area of .
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 .

Ask by Collins Brooks. in the United Kingdom

Mar 30,2025

UpStudy AI · Accepted Answer

Given that the area increases by $$13\%$$ each hour, the multiplication factor per hour is

$$
1 + 0.13 = 1.13.
$$

After $$20$$ hours, the area will be multiplied by $$1.13$$ a total of $$20$$ times. Therefore, the area after $$20$$ hours is given by

$$
\text{Area} = 58 \times (1.13)^{20}.
$$

To compute $$(1.13)^{20}$$, we can use logarithms or a calculator. Approximating, we find

$$
(1.13)^{20} \approx 11.53.
$$

Thus, the area becomes

$$
\text{Area} \approx 58 \times 11.53 \approx 668.9 \text{ m}^2.
$$

Rounding to the nearest $$1$$ m$$^2$$, the area covered in 20 hours will be

$$
669 \text{ m}^2.
$$
After 20 hours, the fire will cover approximately 669 m².