HW 5 Date: Name Use Scantron 882E to transfer the answers. Graph. 1) y = 5x

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1 HW 5 Date: Name Use Scantron 88E to transfer the answers. Graph. ) = 5 ) A) C) D) Differentiate. ) f() = e8 A) e8 8e8 C) 8e D) 8 e 8 ) 3) = e9/ A) 9 e 9/ - e9/ C) 9 e 9/ D) 9 e 9/ 3) ) f() = 9e-3 A) 9e-3-7e-3 C) 7e-3 D) -3e-3 ) 5) f() = -e A) e -8e C) -8e D) -e 5) ) f() = - e- A) + e- e- C) -e- D) - e- ) r

2 7) f() = 7 e 7 7) A) e7 e/7 C) 7e7 D) 7 e 7 8) = e A) 8e 8e C) 8e D) 8e 8) 9) = e8 + 9) A) e + e + C) e + D) e8 + 0) = 5e3 A) 0e3( + 3) 5e3( + 3) C) 5e3(3 + ) D) 0e3(3 + ) 0) ) = ( - + ) e A) ( - ) e ( + ) e ) C) ( + + ) e D) e ) = e - + e ) A) e + e -e + e C) -e - e D) e - e Use calculus to find an critical points and inflection points of the given function. Then determine the concavit of the function and the intervals over which it is increasing/decreasing. 3) f() = e9 3) A) Critical points: none Inflection points: point of inflection at = 0 Concavit: concave down for all < 0 and concave up for all > 0 Critical points: none C) Critical points: none D) Critical points: critical point at = 0 Increasing: increasing for all < 0 and decreasing for all > 0

3 ) f() = e-7 A) Critical points: none Critical points: critical point at = 0 Increasing: increasing for all < 0 and decreasing for all > 0 C) Critical points: none Inflection points: point of inflection at = 0 Concavit: concave down for all < 0 and concave up for all > 0 D) Critical points: none ) 5) f() = - e- A) Critical points: none Critical points: none C) Critical points: none Inflection points: point of inflection at = 0 Concavit: concave down for all < 0 and concave up for all > 0 D) Critical points: critical point at = 0 Increasing: increasing for all < 0 and decreasing for all > 0 5) Find the indicated tangent line. ) Find the tangent line to the graph of f() = e3 at the point (0, ). A) = + = 3 + C) = 3e + D) = ) 7) Find the tangent line to the graph of f() = e-3 at the point (0, ). A) = -8 + = 3 - C) = + D) = 8-7) Solve the problem. 8) The sales in thousands of a new tpe of product are given b S(t) = 0-0e-0.t, where t represents time in ears. Find the rate of change of sales at the time when t = 7. A) - thousand per ear 3.3 thousand per ear C) -3.3 thousand per ear D).0 thousand per ear 8) 3

4 9) A companʹs total cost, in millions of dollars, is given b C(t) = 0-0e-t where t = time in ears. Find the marginal cost when t =. A). million dollars per ear. million dollars per ear C).5 million dollars per ear D). million dollars per ear 9) 0) The demand function for a certain book is given b the function = D(p) = 5e-0.00p. Find the marginal demand Dʹ(p). A) Dʹ(p) = 0.0e-0.00p Dʹ(p) = -0.00e-0.00p C) Dʹ(p) = -0.0pe-0.00p- D) Dʹ(p) = -0.0e-0.00p ) Suppose that the amount in grams of a radioactive substance present at time t (in ears) is given b A(t) = 550e-0.79t. Find the rate of change of the quantit present at the time when t = 7. A).7 grams per ear -.7 grams per ear C) 7.9 grams per ear D) -7.9 grams per ear 0) ) For the given function, find the requested relative etrema or etreme value. ) = 8e + e-; relative etrema A) (0.9, 7.00), relative minimum (-0.9, 8.00), relative minimum C) (-0.9, 5.00), relative maimum D) (-.39,.50), relative minimum ) 3) = e-; relative etrema A) (, /e), relative minimum (, /e), relative maimum C) (-, -e), relative minimum D) (-, -e), relative maimum 3) ) = e7; relative etrema A) (- /7, - e/7), relative maimum (- /7, - /(7e)), relative minimum C) (/7, /(7e)), relative maimum D) (/7, e/7), relative minimum ) 5) = 5e + e; relative etrema A) (, e), relative maimum (5, 0e5), relative maimum C) (-, -e-), relative minimum D) (-5, 0), relative minimum 5) Find the logarithm. Give an approimation to four decimal places. ) ln 80 A) C).553 D) ) 7) ln A) C) D) 7.7 7) 8) ln 95,00,000 A) C) D) ) Solve the eponential equation for t. Round our answer to three decimal places if necessar. 9) et = 78 A) C).0 D).89 9)

5 30) e-t = 0. A) C) -0.7 D) ) 3) e-0.0t = 0.08 A).8.5 C) - D) -.8 3) 3) e0.05t = A) C).0 D) 0 3) Find the derivative of the function. 33) = ln 33) A) - - C) D) 3) = ln ( - ) A) C) - D) - 3) 35) = ln 7 A) + 7 C) D) ) 3) = ln ( + ) A) + C) + D) 3) 37) = ln (3 - ) A) C) - - D) ) Find the derivative. 38) = e ln A) e e (ln + ) C) e ( ln + ) D) e ln 38) 39) = e ln 39) A) e e - e ln ln C) e + e ln D) e ln - e ln Differentiate. 0) = A) (log ) (ln ) C) D) (ln ) 0) 5

6 ) f() = 0 A) (ln )0 0 C) (log 0)0 D) (ln 0)0 ) ) = 0 A) (ln 0) 0 0 (ln ) 0 C) 0 (ln 0) 0 D) 0 (ln ) 0 ) 3) = - A) -- - C) (ln )- D) (-ln )- 3) Find all relative maima or minima. ) = ln - A) (, 0), relative minimum (-, 0), relative minimum C) (, -), relative maimum D) (-, -), relative maimum ) Solve the problem. 5) The sales in thousands of a new tpe of product are given b S(t) = 0-0e-0.9t, where t represents time in ears. Find the rate of change of sales at the time when t =. A) -.5 thousand per ear thousand per ear C).5 thousand per ear D) 95.7 thousand per ear ) The nationwide attendance per da for a certain motion picture can be approimated using the equation A(t) = 3te-t, where A is the attendance per da in thousands of persons and t is the number of months since the release of the film. Find and interpret the rate of change of the dail attendance after months. A).905 thousand persons/da month; the change in the dail attendance is increasing thousand persons/da month; the change in dail attendance is decreasing. C) 3.8 thousand persons/da month; the dail attendance is increasing. D) thousand persons/da month; the dail attendance is decreasing. 5) ) For the given function, find the requested relative etrema or etreme value. 7) = e + 7e-; relative etrema A) (0.3,.8), relative maimum (.5, 3.50), relative minimum C) (-0.3,.), relative minimum D) (0.3, 7.8), relative minimum 7) 8) = e5; relative etrema A) (/5, /(5e)), relative maimum (- /5, - /(5e)), relative minimum C) (/5, e/5), relative minimum D) (- /5, - e/5), relative maimum 8) 9) = e + e; relative etrema A) (7, 3e7), relative maimum (-7, -e-7), relative minimum C) (, e), relative maimum D) (-, 0), relative minimum 9)

7 Solve the problem. 50) The population of a particular cit (in thousands) can be modeled b the function 500 P(t) = + 0e-0.05, where is the number of ears after 90. In what ear was the growth rate of the population the fastest? A) C) 980 D) ) 7

Math Want to have fun with chapter 4? Find the derivative. 1) y = 5x2e3x. 2) y = 2xex - 2ex. 3) y = (x2-2x + 3) ex. 9ex 4) y = 2ex + 1

Math Want to have fun with chapter 4? Find the derivative. 1) y = 5x2e3x. 2) y = 2xex - 2ex. 3) y = (x2-2x + 3) ex. 9ex 4) y = 2ex + 1 Math 160 - Want to have fun with chapter 4? Name Find the derivative. 1) y = 52e3 2) y = 2e - 2e 3) y = (2-2 + 3) e 9e 4) y = 2e + 1 5) y = e - + 1 e e 6) y = 32 + 7 7) y = e3-1 5 Use calculus to find