Question 3 Let P (t) be a deer population (in thousands) of an ecological region t years after 2000. A graph of the derivative P' (t) is give below. Use it to answer the following questions. 2 (a) Calculate P'(8) and interpret that in terms of the deer population. (b) Indicate the years during which the deer population declined. (c) Order the following from least to greatest. If there is a tie, indicate that with an equals sign. You do not need to find the values themselves: P'(1), P'(3), P'[6), P'(7), P'(9), P'(10). ((1) Order the following from least to greatest. If there is a tie, indicate that with an equals sign. You do not need to find the values themselves: 13(0), P(2), P(3), P(5), P(7), P(9). (0) Order the following from least to greatest. If there is a tie, indicate that with an equals sign. You do not need to nd the values themselves: 13(9), P(11), P(14), P(15). f f (f) Evaluate the limit lim w. htU it Question 4 Ultrasound is often used to make images of developing fetuses. In particular, by measuring the size of a fetus ultrasound technicians can estimate its age and then predict its birthdate. To do this requires formulas for fetus size as a function of age. Verbung et al. (2008) t data from over 6000 fetal ultrasounds. They measured the femur length, L, (in mm) as a function of the fetus age, t, (in weeks) and found the following formula: L 2 37.50 + 3.71t 6.33 X 10'4t3. (a) Calculate the rate of growth, dL/dt, at t :15, 20, and 30 weeks. Does the rate of growth of the fetus increase or decrease as it ages? (b) Write a sentence interpreting L'(15) in terms of the femur length, including units. Question 5 The revenue per month earned by the Couture clothing chain at time t is R=Nm where N (t) is the number of stores and S (t) is the average revenue per store per month. Couture releases a statement to their investors saying that currently they have 50 stores with a total revenue of $7,500,000 and expect to increase the number of stores by about 2 stores per month and increase total revenue by about $250,000 per month. What does this statement imply about the current rate of change of the average revenue per store per month