Congresswoman Celesta Gomez has just come out in favor of a controversial bill. A poll suggests that t days after she declares her position on the bill, the percentage of her constituency (those who favor her at the time she declares her position) that still supports her is

The vote is to be taken 10 days after she announces her position.

a. Sketch the graph of S(t) for 0 t 10.

b. When is the congresswoman’s support at its lowest point? What is the minimum support level?

c. The derivative S'(t) may be thought of as an approval rate. Is the congresswoman’s approval rate positive or negative when the vote is taken? Is the approval rate increasing or decreasing at this time? Interpret your results.

Transcribed Image Text:

S(t) 100(² - 3t+25) t² + 7t + 25