Questions: The expression 5 * 1.15^t gives the area, in square meters, damaged by a fire as a function of minutes since the fire was discovered. What does 5 represent in this expression? Choose 1 answer: (A) The area damaged by the fire is multiplied by 5 each minute. (B) An area of 5 square meters had been damaged by the fire by the time it was discovered. (C) It has been 5 minutes since the fire was discovered.

Solution Steps

The expression \(5 \cdot 1.15^{t}\) represents the area damaged by the fire as a function of time \(t\) in minutes. The constant 5 in this expression represents the initial area damaged by the fire at the time it was discovered. Therefore, the correct answer is (B) An area of 5 square meters had been damaged by the fire by the time it was discovered.

The expression \(5 \cdot 1.15^{t}\) models the area damaged by a fire as a function of time \(t\) in minutes. Here, \(5\) is a constant that plays a crucial role in determining the initial conditions of the model.

In this expression, the constant \(5\) represents the area that was damaged by the fire at the moment it was discovered, which is the initial time \(t = 0\). Therefore, when \(t = 0\), the area damaged is calculated as: \[ \text{Area} = 5 \cdot 1.15^{0} = 5 \cdot 1 = 5 \text{ square meters} \]

Thus, the interpretation of the constant \(5\) is that it signifies the area damaged by the fire at the time it was discovered.

Final Answer