a company determines that its weekly online sales, ( s(t) ), in hundreds of dollars, ( t ) weeks after…

Explanation:

Step1: Recall the average value formula

The average value of a function (y = f(x)) over the interval ([a,b]) is (\frac{1}{b - a}\int_{a}^{b}f(x)dx). Here, (a = 0), (b=7), and (S(t)=62e^{t}). So the average value (\bar{S}=\frac{1}{7-0}\int_{0}^{7}62e^{t}dt).

Step2: Integrate the function

We know that (\int e^{t}dt=e^{t}+C). Then (\frac{62}{7}\int_{0}^{7}e^{t}dt=\frac{62}{7}[e^{t}]_{0}^{7}).

Step3: Evaluate the definite - integral

Using the fundamental theorem of calculus (F(b)-F(a)) (where (F(t)) is an antiderivative of (f(t))), we have (\frac{62}{7}(e^{7}-e^{0})). Since (e^{0} = 1), it is (\frac{62}{7}(e^{7}- 1)). Now, (e^{7}\approx1096.633). Then (\frac{62}{7}(1096.633 - 1)=\frac{62\times1095.633}{7}\approx\frac{67929.246}{7}\approx9704.18) (in hundreds of dollars).

Answer:

(9704.18) (in hundreds of dollars)