Question

the number of mybook members, in millions, can be approximated by the function ( s(t) = 15t^2 - 77t + 106 ) where ( t ) is the number of years since 2010. how is the number of mybook members changing in the year 2017? (round your answer to a whole number.)

Explanation:

To determine how the number of Mybook members is changing in 2017, we need to find the rate of change of the function \( S(t) = 15t^2 - 77t + 106 \) at \( t \) corresponding to 2017.

First, we find the value of \( t \) for the year 2017. Since \( t \) is the number of years since 2010, we calculate:
\[
t = 2017 - 2010 = 7
\]

Next, we find the derivative of \( S(t) \) to get the rate of change function. The derivative of \( S(t) \) with respect to \( t \) is:
\[
S'(t) = \frac{d}{dt}(15t^2 - 77t + 106)
\]
Using the power rule for differentiation (\( \frac{d}{dt}(t^n) = nt^{n-1} \)):
\[
S'(t) = 30t - 77
\]

Now, we evaluate the derivative at \( t = 7 \):
\[
S'(7) = 30(7) - 77
\]
\[
S'(7) = 210 - 77
\]
\[
S'(7) = 133
\]

Answer:

The number of Mybook members is changing at a rate of 133 million members per year in 2017.