College

The area covered by a fire increases by [tex]$13 \%$[/tex] each hour. Currently, the fire covers an area of [tex]$58 \, \text{m}^2$[/tex].

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 [tex]$1 \, \text{m}^2$[/tex].

Answer :

We start with an initial area given by

$$
A_0 = 58 \text{ m}^2.
$$

Each hour, the area increases by 13%, which means the area is multiplied by

$$
1 + 0.13 = 1.13
$$

every hour. Thus, after 20 hours, the area covered by the fire is given by the exponential growth formula

$$
A = A_0 \cdot \left(1.13\right)^{20}.
$$

Substituting the initial value, we have

$$
A = 58 \cdot \left(1.13\right)^{20}.
$$

Evaluating the expression gives an exact area of approximately

$$
668.3390903539545 \text{ m}^2.
$$

Rounding to the nearest $1 \text{ m}^2$, the area is

$$
668 \text{ m}^2.
$$

Thus, the fire will cover approximately $668 \text{ m}^2$ in 20 hours.

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