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
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) 3 3 + + 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
) 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) = 3 + 3 ) 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
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).07 0.90 C).553 D) 5.930 ) 7) ln 0.0008 A) 3.388-7.7 C) -3.388 D) 7.7 7) 8) ln 95,00,000 A) 8.373.807 C) 7.9795 D) 0.053 8) Solve the eponential equation for t. Round our answer to three decimal places if necessar. 9) et = 78 A).357 8.705 C).0 D).89 9)
30) e-t = 0. A) 0.9-0.9 C) -0.7 D) -.087 30) 3) e-0.0t = 0.08 A).8.5 C) - D) -.8 3) 3) e0.05t = A) 0.035 3.83 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) + 7 35) 3) = ln ( + ) A) + C) + D) 3) 37) = ln (3 - ) A) - - - C) - - D) - 3-37) 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
) 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 -95.7 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. -3.8 thousand persons/da month; the change in dail attendance is decreasing. C) 3.8 thousand persons/da month; the dail attendance is increasing. D) -.905 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)
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) 970 90 C) 980 D) 990 50) 7