t(hours). 1 2 4 7 8

R(t)(views/hour). 20 301 99 2 1

A post is viewed at a rate modeled by R(t) views per hour

R is continuous

t is the number of hours since the post was made (t=0)

a. Approximate R'(3) using the average rate of change of R over 2<= t <= 4. Assume the approximation calculated actually equals R'(3). Explain the meaning of R'(3) in the context of this question with units.

b. Interpret what integral R(t)dt from 1 to 8 in the context. Use a left Riemann sum with the four intervals from the data to approximate the integral R(t)dt from 1 to 8

c. A second post is made at t=0. For t >= 0, the total views that the post received t hours since the post was made is modeled by V(t)=-210+8401+3e^-0.6t. Find L=limt t -> V(t). Explain the limit calculated in the context.

d. With the same V(t) function, we know that V(4)=450.297, V(7)=593.838, and V'(7)=20.763. According to R and V, is there a time for 4 <=t<=7 when the two posts are viewed at the same rate? Explain