Management Calculus Exam 2 Fall 2020 Read the instructions carefully: Show all your work for partial credit

Management Calculus Exam 2 Fall 2020
Read the instructions carefully:
Show all your work for partial credit.
Answers with no supporting work will be given no credit.
Be sure to simplify your final answers. Use positive exponents.
Label answers with the correct units where appropriate.
1. (10 pts each) Find the derivative :
A. ???? = −3????(5???? + 4)6
B. ???? =
(2????+3)4
(3????−2)5
2. (12 pts) A total revenue function is given as ????(????) = 1000√????2 − 0.1???? , x is the number of units sold. Find the rate at
which the total revenue is changing when 25 units have been sold. (Round to 2 decimal places where needed)
3. The total cost, in dollars, is given by ????(????) = 200 − 40????−????
where x is the number of units built and 0 ≤ ???? ≤ 5.
A. (8 pts) Find the marginal cost, ????’(????).
B. (4 pts) Find ????’(1). (Round to 2 decimal places)
C. (6 pts) Sketch ????(????).
D. (4 pts) Find lim????→∞ ????(????).
4. Given ????(????) = ????????(4????2
− 3) .
A. (8 pts) Find the slope of the tangent at x=1.
B. (4 pts) Find the equation of the tangent line at x=1.
C. (4 pts) Draw a graph of f(x) and include the tangent line at x=1.
5. The amount , A(t), represents the amount Americans spent on organic food (in billions of dollars) t years after
2014. A(t) can be approximated by the equation:
????(????) = 35.8????0.104????
A. (4 pts) Estimate the amount Americans spent on organic food in 2017. (Round to 2 decimal places)
B. (6 pts) When will the amount that Americans spend on organic foods reach $60 billion? Round to the
nearest year.
C. (10 pts) How fast is the amount spent on organic foods increasing in 2017? (Round to 2 decimal places)
6. Iodine-131 has a decay rate of 9.6% per day. The rate of change in the amount of Iodine-131 after t days is given by
????????
????????
= −0.096????.
A. (4 pts) If ????0 is the amount present at t=0, find the exponential function that models the decay.
B. (6 pts) If the initial amount of Iodine is 500 g, how much remains after 6 days? (Round to 2 decimal places)