Is there a time t , for 1<t<8 , at which the rate of change of the number of people at the venue changes from negative to positive? Give a reason for your answer.

Question

For time 0≤t≤8, people arrive at a venue for an outdoor concert at a rate modeled by the function A defined by A(t)=0.3sin(1.9t)+0.3cos(0.6t)+1.3. For time 0≤t≤1, no one leaves the venue, and for time 1≤t≤8, people leave the venue at a rate modeled by the function L defined by L(t)=0.2cos(1.9t)+0.2sint+0.8. Both A(t) and L(t) are measured in hundreds of people per hour, and t is measured in hours. The number of people at the venue, in hundreds, at time t hours is given by P(t).

Answer 1

Determine the value of t, 1 ≤ t ≤ 8, such that A(t) - L(t) = 0.