Question

the number of mybook members, in millions, can be approximated by the function $s(t)=15t^{2}-72t + 104$ 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:

Step1: Determine the value of t

The year is 2017 and t is the number of years since 2010. So $t = 2017 - 2010=7$.

Step2: Find the derivative of the function

The function is $S(t)=15t^{2}-72t + 104$. Using the power - rule for differentiation, if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$. The derivative $S^\prime(t)=30t-72$.

Step3: Evaluate the derivative at t = 7

Substitute $t = 7$ into $S^\prime(t)$. $S^\prime(7)=30\times7-72$.
$S^\prime(7)=210 - 72=138$.

Answer:

138