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Question : In an epidemiological model used to study the spread of drug use, a single drug : 2151803

**Find the area between the graph of the function and the x-axis over the given interval, if possible.**

30) f(x) = (11/(x - 1)^{2}) for (-∞, 0]

A) 11

B) 1

C) -11

D) Divergent

31) f(x) = (3/(x - 1)^{3}) for (-∞, 0]

A) -1.5

B) -0.5

C) 1.5

D) Divergent

32) f(x) = 6e^{-x} for (-∞, e]

A) -0.396

B) 0.396

C) -90.924

D) Divergent

33) f(x) = (14/x - 1) for (-∞, 0]

A) 0

B) 14

C) -14

D) Divergent

34) f(x) = (x/(1 + x^{2})^{5}) for (-∞, ∞)

A) (1/8)

B) - (1/8)

C) 0

D) Divergent

35) f(x) = x^{4} e^{-x^5} for (-∞, ∞)

A) 0

B) - (1/5)

C) (1/5)

D) Divergent

36) f(x) = (1/x + 1) for (-1, ∞)

A) ln 1

B) (1/1)

C) 1

D) Divergent

37) f(x) = (1/(x + 3)^{5}) for (-3, ∞)

A) (5/3)

B) (3/5)

C) (1/6)

D) Divergent

38) f(x) = (1/x^{4.2}) for (1, ∞)

A) (5/16)

B) (21/26)

C) (5/26)

D) Divergent

**Solve the problem. Round your answer to the nearest whole number.**

39) The capital value of an asset is defined as , where k is the annual rate of interest compounded continuously and R(t) gives the annual rate at which earnings are produced by the asset at time t. Find the capital value of an asset that produces $5000 yearly income at 4% compounded continuously.

A) $100,000

B) $125,000

C) $150,000

D) $130,000

40) The capital value of an asset is defined as , where k is the annual rate of interest compounded continuously and R(t) gives the annual rate at which earnings are produced by the asset at time t. Find the capital value of an asset that produces $5000 yearly income at 5% compounded continuously.

A) $83,333

B) $95,000

C) $125,000

D) $100,000

41) The capital value of an asset is defined as , where k is the annual rate of interest compounded continuously and R(t) gives the annual rate at which earnings are produced by the asset at time t. Find the capital value of an asset that produces $5000 yearly income at 6% compounded continuously.

A) $85,000

B) $80,000

C) $100,000

D) $83,333

42) The capital value of an asset is defined as , where k is the annual rate of interest compounded continuously and R(t) gives the annual rate at which earnings are produced by the asset at time t. Find the capital value of an asset that produces $5000 yearly income at 7% compounded continuously.

A) $75,000

B) $83,333

C) $70,000

D) $71,429

43) The capital value of an asset is defined as , where k is the annual rate of interest compounded continuously and R(t) gives the annual rate at which earnings are produced by the asset at time t. Find the capital value of an asset that produces $5000 yearly income at 8% compounded continuously.

A) $71,429

B) $62,500

C) $65,000

D) $60,500

44) The capital value of an asset is defined as , where k is the annual rate of interest compounded continuously and R(t) gives the annual rate at which earnings are produced by the asset at time t. Find the capital value of an asset that produces $5000 yearly income at 9% compounded continuously.

A) $55,556

B) $50,000

C) $62,500

D) $55,000

45) The capital value of an asset is defined as , where k is the annual rate of interest compounded continuously and R(t) gives the annual rate at which earnings are produced by the asset at time t. Suppose an asset produces a perpetual stream of income with a flow rate of R(t) = 1200 e^{(0.03t)} . Find the capital value at an interest rate of 7% compounded continuously.

A) $17,142

B) $40,000

C) $12,000

D) $30,000

46) The capital value of an asset is defined as , where k is the annual rate of interest compounded continuously and R(t) gives the annual rate at which earnings are produced by the asset at time t. Suppose income from an investment starts (at time 0) at $8000 a year and increases linearly and continuously at a rate of $300 per year. Find the capital value at an interest rate of 6% compounded continuously.

A) $133,333

B) $2,222,222

C) $216,667

D) $138,333

47) The rate of a reaction to a drug is given by r'(t) = 7t^{2}e^{-t}, where t is the number of hours since the drug was administered. Find the total reaction to the drug over all the time since it was administered, assuming this is an infinite time interval. (Hint: t^{k}e^{-t} = 0 for all real numbers k.)

A) 14

B) ∞

C) 49

D) 0

48) In an epidemiological model used to study the spread of drug use, a single drug user is introduced into a population of N non-users. Under certain assumptions, the number of people expected to use drugs as a result of direct influence from each drug user is given by

S = N,

where b and k are constants. Find the value of S.

A) N(1 - e^{-kt})e^{-bt}

B) 4N/[b(b + k)]

C) 4N/(b + k)

D) 4Ne^{-bkt}

49) Radioactive waste is entering the atmosphere over an area at a decreasing rate. Use the improper integral with P = 17 to find the total amount of waste that will enter the atmosphere for k = 0.06.

A) 283

B) 102

C) 2830

D) 28

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

**Provide the proper response.**

50) A student wishes to find the integral of a function that has the property limit f(x) = 1. Why can this not be done?

51) A student wishes to take the integral over all real numbers of f(x) = {(x^{2} if x < 0)

(1/x), if x > 0), and claims this is zero because -∞ + ∞ equals zero. What is wrong with this thinking?

52) A student claims that always exists, as long as a and b are both positive. Refute this by giving an example of a function for which this is not true.

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

53) A student knows that = 20. Can be found, and if so, what is it?

A) Yes, -20

B) No

54) A student knows that diverges, but needs to investigate , where g(x) = (f(x)/6) Does this integral necessarily also diverge?

A) No

B) Yes

55) A student knows that converges. Does also necessarily converge?

A) No

B) Yes

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

56) A student needs . Is this integral the same as 2 and if so, why?