Questions: Using a calculator to evaluate the appropriate integral, find the average value of P=f(t)=2.06(1.04)^t for 0 ≤ t ≤ 25. Average value of P=

Solution Steps

To find the average value of the function \( P = f(t) = 2.06(1.04)^t \) over the interval \( 0 \leq t \leq 25 \), we need to:

1. Compute the definite integral of \( f(t) \) from 0 to 25.
2. Divide the result by the length of the interval, which is 25.

We are given the function \( P = f(t) = 2.06(1.04)^t \) and the interval \( 0 \leq t \leq 25 \).

To find the average value of the function over the interval, we first compute the definite integral of \( f(t) \) from 0 to 25: \[ \int_{0}^{25} 2.06(1.04)^t \, dt \] The value of this integral is approximately \( 87.4952 \).

The average value of the function over the interval is given by dividing the integral by the length of the interval: \[ \text{Average value} = \frac{1}{25} \int_{0}^{25} 2.06(1.04)^t \, dt = \frac{87.4952}{25} \approx 3.4998 \]

Final Answer