Crystal

Mathematics

27 June, 07:59

Use the following information for Questions 1-3:

The rate at which water flows into a tank, in gallons per hour, is given by a differentiable function R of time t. The table below gives the rate as measured at various times in an 8-hour time period.

t (hours) 0 2 3 7 8

R (t) (gallons per hour) 1.95 2.5 2.8 4 4.26

2.) Is there some time t, 0 < t < 8, such that R′ (t) = 0? Justify your answer.

3.) The rate of water flow R (t) can be estimated by W (t) = ln (t2 + 7). Use W (t) to approximate the average rate of water flow during the 8-hour time period. Indicate units of measure.