Final answer:
The question involves calculating the area of a fire after one hour given a 13% hourly growth rate. Starting with an area of 58 m², we use the formula A = A_0 (1 + r)^t to find that the fire will cover an area of approximately 65.54 m² after one hour.
Step-by-step explanation:
The question asks about the rate at which the area covered by a fire increases. We use concepts from exponential growth to solve this problem. With a current area of 58 square meters and an increase of 13% each hour, we apply the formula for exponential growth:
A = A_0 (1 + r)^t
where:
- A is the final area,
- A_0 is the initial area (58 m²),
- r is the rate of growth (0.13), and
- t is the time in hours.
To find the area after one hour, we plug the values into the equation:
A = 58 * (1 + 0.13)¹ = 58 * 1.13 = 65.54 m²
Therefore, after one hour, the fire will cover an area of approximately 65.54 square meters.