mth135.

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MTH 135 Participation Assignment Week 4 – Aug 4 2021

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

1) Consider the function: Choose the answer choice that includes all of the pair(s) of functions from the

list so that f(x) can be written as a composition:

1) _______

A) B) g(x) = ;h(x) =

C) g(x) = ;h(x)= D) Both A and B

Find the derivative.

2) Find: 2) _______

A) B)

C) 8 D) 448

Provide an appropriate response.

3) Find for y = ln ( 3x3 - x2) 3) _______

A) B) C) D)

Solve the problem.

4) The concentration of a certain drug in the bloodstream t minutes after swallowing a pill containing the drug can be

approximated using the equation where C(t) is the concentration in arbitrary units and t is in

minutes. Find the rate of change of concentration with respect to time at t = 8 minutes. 4) _______

A) - units/min B) - units/min C) - units/min D) - units/min

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Provide an appropriate response.

5) Find x' for x = x(t) defined implicitly by and evaluate x' at 5) _______

A) B)

C) D)

6) Find y' and the slope of the tangent line to the graph of 6) _______

A) B) C) D)

Solve the problem.

7) The position of a particle at time t is given by s, where . Find the velocity 7) _______

A) ds/dt = B) ds/dt =

C) ds/dt =

D) ds/dt =

Provide an appropriate response.

8) Suppose two automobiles leave from the same point at the same time. If one travels north at 60 miles per hour and the

other travels east at 45 miles per hour, how fast will the distance between them be changing after three hours?

8) _______

A) 50 mph B) 150 mph C) 125 mph D) 75 mph

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

9) Find the relative rate of change of f(x) = 15x + 2x ln x 9) _____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent.

10) f(x) = 4500 - 4 ; x = 20 10) ______

A) 3.6% B) -5.5% C) 5.5% D) -1.0%

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Find the elasticity of the demand function as a function of p.

11) x = D(p) = 11) ______

A) E(p) = B) E(p) =

C) E(p) = D) E(p) = 1,000p(p + 8)

Use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p.

12) x = f(p) = 2005 - ; p = 13 12) ______

A) Inelastic B) Elastic C) Unit elasticity

Use the price-demand equation to find the values of p which meet the given condition of elasticity.

13) x = f(p) = 216-2 ; determine the values of p for which demand is elastic and the values of p for which demand is

inelastic.. 13) ______

A) Elastic on (0, 6), inelastic on (6, 108) B) Elastic on (6, 108), inelastic on (0, 6)

C) Elastic on (0, 6), inelastic on (6, 6 ) D) Elastic on (6, 6 ), inelastic on (0, 6)

Use the demand equation to find the revenue function.

14) x = f(p) = 55 - 7 14) ______

A) R(p) = 55p - 7 B) R(p) = 55p - 7

C) R(p) = 55p - 7p D) R(p) = 55p - 49

Solve the problem.

15) A beverage company works out a demand function for its sale of soda and finds it to be

x = D(p) = 2,900 - 21p

where x = the quantity of sodas sold when the price per can, in cents, is p. At what prices, p, is the elasticity of demand

inelastic? 15) ______

A) For p > 276 cents B) For p < 138 cents C) For p > 30,450 cents D) For p < 69 cents