Question

The amount of money raised during a competing fund-raising campaign is modeled by the function M defined by M(t)=240(2t−1)(2t+36), where M(t) is measured in United States dollars and t is the time in days since that campaign began. According to this model, is there a time t, for 0≤t≤2, at which the amount of money raised is 10 dollars? Justify your answer.

Answer 1

Explanation:

If the amount of money raised during a competing fund-raising campaign is modeled by the function M defined by M(t)=240(2t−1)(2t+36), where M(t) is measured in United States dollars and t is the time in days, to get the time t if the money raised is 10 dollars, we will substitute M = 10 into the modeled function and calculate the value of t

M(t)=240(2t−1)(2t+36)

10=240(2t−1)(2t+36)

1 = 24(2t−1)(2t+36)

open the parenthesis

1 = 24(4t²+72t-2t-36)

1 = 96t²+1680t-864

96t²+1680t-865 = 0

On factorizing, t = 2 is not a factor of the expression. Hence there is not a time within the interval 0≤t≤2, at which the amount of money raised is 10 dollars