Math 127 Fall 2010 Exam #1 A 1. Calculate f (1 h)  f (1)h for f(x)= 3x  1 (a) 32 (b) 32  h (c) 121h (d) 32 2  h  (e) 34 h 2. Suppose D(t)=10t2 – 5 gives the distance an object falls (in meters) from a tower in t seconds. What is the average speed of the object over the interval t=1 to t=3 seconds? (a) 40 m/s (b) 30 m/s (c) 80 m/s (d) 27 m/s (e) 15 m/s 3. Suppose f(x) is a linear function with f(2)=11 and f(4)=19. Calculate f(-1). (a) 1 (b) -1 (c) 0 (d) 2 (e) -4 4. Each day Jim’s Hots sells hot dogs for at a price of $2.50 per hot dog. The daily fixed cost is $50 and the marginal cost is $0.50 per hot dog. How many hot dogs must Jim’s Hots sell each day in order to break even? (a) 50 (b) 35 (c) 40 (d) 20 (e) 255. Suppose a demand curve is given by: q=60,000 – 1000p and the corresponding supply curve is given by: q=5000p for q>0. Find the equilibrium point (po, qo) (a) (20, 120000) (b) (10, 50000) (c) (5, 30000) (d) (1, 6000) (e) (15, 45000) 6. Suppose f and g are given by the following tables: x 1 2 3 4 5 x 1 2 3 4 5 f(x) 6 1 -4 -9 -14 g(x) 2 8 32 128 512 These function values indicate: (a) f and g both change linearly (b) f and g both change exponentially (c) f declines exponentially while g grows linearly (d) f declines linearly while g grows exponentially (e) none of these statements is true 7. The population of Metropolis is growing exponentially according to the formula: P(t)=450,000(1.035) t. Approximately how many years will it take for the population to reach 1,000,000? (a) 25.2 years (b) 18.6 years (c) 21.1 years (d) 0.77 years (e) 23.2 years8. Solve the equation: 400 10  (5t) (a) t = ln(5/40) (b) t = ln(40) – ln(5) (c) t = ln(10) – ln(40/5) (d) t = (ln40)/ln(5) (e) t = (ln5)/(ln40) 9. Suppose a pile of radioactive waste is buried in a deep cave in Nevada, and the material has a half-life of 800 years. How long will it take for this material to be 99% decayed (so that only 1% of the original amount remains)? (a) 2658 years (b) 5315 years (c) 8712 years (d) 4620 years (e) 9970 years 10. If I place $15,000 into an investment account that pays 4% interest per year compounded annually, how long will it take for the investment to reach $31,111? (a) 17.3 years (b) 18.6 years (c) 14.2 years (d) 11.6 years (e) 1.7 years 11. Suppose that you would like to go to Paris seven years from now, and you have calculated that you will need $8,000 at that time for the trip you’d like to take. If you have an account that pays 5% interest compounded continuously, how much should you deposit today in order to reach your goal of $8,000 in seven years? (a) $5637.50 (b) $4291.10 (c) $6046.27 (d) $3894.10 (e) $1271.3512. Given that f(x) = 3x3 + 2x2 +6 and g(x) = 4x + 2, find f(g(0)). (a) 26 (b) 38 (c) 6 (d) 8 (e) 0 13. The blood mass of a mammal is proportional to its body mass. A rhinoceros with body mass 3000 kg has a blood mass of 150 kg. What is the blood mass of a human with a body mass of 60 kg? (a) 1200 kg (b) 3 kg (c) 20 kg (d) 150 kg (e) 375 kg 14. Suppose y=g(x) is a function defined for x between 1 and 5 such that: x 1 2 3 4 5 g(x) 2 4 7 5 1 Using the table, find the best estimate of g’(4). (a) 3 (b) -2 (c) -4 (d) -6 (e) -315. Suppose y=g(x) has the following graph: a b c d e f Then the derivative function g’(x) is negative on which interval? (a) {x: e<x<f} (b) {x: a<x<d} (c) {x: a<x<b} and {x: e<x<f} (d) {x: b<x<e} (e) {x: d<x<f} 16. Given the following graph of h(x), x1 x2 x3 x4 x5 x6 which of the following has the greatest value? (a) h’(x3) (b) the average rate of change of h from x1 to x3 (c) h’(x1) (d) h(x4) – h(x5) (e) the average rate of change of h from x2 to x417. Let w(x) be the weight of a spaceship in kilograms and let x be the altitude of the spaceship in miles. Then w’(x) will be measured in what units? (a) miles (b) kilograms (c) miles per kilogram (d) kilograms per mile (e) (miles)2 18. Given the graph of g(x) shown below: a b c d e f Which of the following is FALSE? (a) g’(a)≥0 (b) g’’(b)≤0 (c) g(c)≥0 (d) g’’(d)≤0 (e) g’(c)≤019. Let g(x) =1.7 x. We want to approximate g’(2). If we do this using the interval from 2 to 2+h, where h=0.001, the resulting approximation will be: (a) 1.2499 (b) 1.5339 (c) 1.2955 (d) 1.6085 (e) 1.4767 20. Let c(q) represent the total cost of producing q widgets. If C(10) = 200 and C’(10) = 15, then use the local linear approximation to estimate the total cost of producing 7 widgets. (a) $245 (b) $305 (c) $255 (d) $155 (e)