Download Applied Calculus Exam 1 Solutions by Prof. Brick and more Exams Calculus in PDF only on Docsity! Prof. S. Brick Math 120 Summer ’02 Applied Calculus; Exam 1 section 11 1. You are driving slowly to your favorite class – Math 120, of course – when you realize that you have forgotten your bag lunch. You turn around and start to drive very fast back home, but a police car pulls you over. You manage to use Calculus to convince the policeman to refrain from giving you a ticket, though it does take you some time. You then drive slowly home where you very quickly get the lunch. Before you can leave to go to your Calculus class, your Mom tells you take your little sister to her Ballet class, which is in the opposite direction from school. You drive very fast to the Ballet class, teasing your sister and eating your lunch, and drop her off, practically without even coming to a complete stop. You then drive even faster towards school. You get halfway there (halfway as measured from the Ballet class) but your luck fails you as the very same policeman from earlier pulls you over for speeding. You start ranting and raving about Ballet, Calculus and chocolate-covered space aliens, when all of sudden and for no apparent reason, he takes you away for observation (we won’t even speculate on why). Let f(t) be the distance you are from your favorite place in the world: your Calculus class, where t is time with t = 0 being the time you start this adventure and t = A being the time you are taken away (note that f(t) is not the distance you have travelled). Sketch a graph of f(t) for 0 ≤ t ≤ A. Label the various sections of the graph. 2. You make math T-shirts. You have fixed costs of $100 and variable costs of $6 per shirt. Find the cost equation. If you sell the shirts for $10 each, find the revenue function. Graph both of them on a single graph and find the break-even point. Label it on the graph. 3. You are selling iced cappuccino’s. If you charge one dollar, you end up making 200 sales every week. Each dime increase in price results in 10 fewer sales. Assuming it is linear, find and graph the demand curve (with quantity on the horizontal axis and price in dollars). 4. Suppose f(10) = 80 and f(40) = 20. Find two possible values for f(70), one if f is linear and the other if f is exponential. 5. The half-life of Mobilium is 7 hours. How long before 18 grams decays into 2 grams 6. Let C(r) be the total cost of paying off a car loan where r is the interest rate in percentage points. What are the units of C ′(r) ? What would C ′(10) = $700 mean ? 7. Suppose you know for a fact that the derivative of f(x) = √ x is f ′(x) = 1 2 √ x . Find the equation of the tangent line at x = 9. 8. Suppose MR(100) = 40 and MC(100) = 24. Estimate the additional profit made by increasing the production to a level of q = 106. 9. Sketch a graph of a (single) function with f(2) = −10, f ′(2) = +4 and f ′′(2) < 0 and f(6) = 3, f ′(6) = −5 and f ′′(6) > 0.
