Non$-$calculator section:

The weight of a baby elephant grows rapidly during the first several days after birth. The rate

of weight gain can be modeled as a monotonic increasing, differentiable function $W(t),$ and

select values of this function are given in the table:

a$)$ What is the average rate of change of the rate of weight gain of a baby elephant over the first

$11$ days after birth? Use correct units and interpret your answer in the context of the question.

b$)$ Is there a time in between $t=0$ and $t=11$ days such that the rate of weight gain of baby

elephants is exactly equal to $10$ pounds$/$day$?$ Justify your answer.

c$)$ The average baby elephant is $200$ pounds at birth $(t=0).$ Use a right Riemann sum with $4$

intervals to estimate the weight of a baby elephant when it is $11$ days old.

d$)$ Will your answer in part $c$ be an overestimate or an underestimate? Justify your answer.