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Question : An investment is expected to produce a uniform continuous rate of money flow of $500 per year for 10 years : 2163455

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

23) Approximate dx; n = 4, by (a) Simpson's rule and (b) the trapezoidal rule.

Enter your answers in that order as just unlabeled real numbers rounded to two decimal places, separated by a comma.

24) Approximate dx; n = 6, by (a) Simpson's rule and (b) the trapezoidal rule.

Enter your answers in that order as just unlabeled real numbers rounded to two decimal places, separated by a comma.

25) Approximate dx; n = 4, by (a) Simpson's rule and (b) the trapezoidal rule.

Enter your answers in that order as just unlabeled real numbers rounded to two decimal places, separated by a comma.

26) Approximate dx; n = 4, by (a) Simpson's rule and (b) the trapezoidal rule.

27) Approximate dx; n = 6, by (a) Simpson's rule and (b) the trapezoidal rule.

28) Calculate (a) the trapezoidal approximation and (b) Simpson's approximation to where f is the tabulated function.

Enter your answers in that order as just unlabeled real numbers rounded off to two decimal places, separated by acomma.

29) Calculate (a) the trapezoidal approximation and (b) Simpson's approximation to where f is the tabulated function.

Enter your answers in that order as just unlabeled integers separated by acomma.

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

Use n = 4to approximate the value of the integral by Simpson's rule.

30)

A) 131.5

B) 142.7

C) 28.5

D) 140.7

Solve the problem. Round your answer, if appropriate.

31) Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use Simpson's rule to approximate the distance traveled by the car in the 8 seconds.

A) 177.50 feet

B) 132.00 feet

C) 178.33 feet

D) 176.33 feet

32) The following table shows the rate of water flow (in gal/min) from astream into a pond during a 30-minute period after a thunderstorm. Use Simpson's rule to estimate the total amount of water flowing into the pond during this period.

A) 11,475 gallons

B) 9050.0 gallons

C) 9975 gallons

D) 9983.3 gallons

Solve the problem.

33) Consider where f(x) = (1/20)x^{5} + 3x^{2}. Find a number A such that |f''(x)| ≤ A for all x satisfying 0 ≤ x ≤ 2. Use this A to obtain a bound on the error of using the midpoint rule with n = 4to approximate the definite integral.

A) 0.1250

B) 0.2917

C) 1.4583

D) 0.0365

34) Consider where f(x) = e^{-3x}. Find a number A such that |f''''(x)| ≤ A for all x satisfying 0 ≤ x ≤ (1/3). Use this A to obtain a bound on the error of using Simpson's rule with n = 2to approximate the definite integral.

A) 7.2338 × 10-6

B) 6.5104 × 10-5

C) 2.8935 × 10-5

D) 1.0417 × 10-2

35) Suppose the annual rate of income from an investment at any time t is K(t) = -100 + 50t. What is the formula for the present value of the income over the next 5 years at a 6% interest rate compounded continuously?

A)

B)

C)

D)

E) none of these

36) If the annual rate of return from an investment is -3000 + 125t, find the present value of the income generated in the third year if the interest rates are 8.5%.

A)

B)

C)

D)

E) none of these

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

37) A company estimates that the rate of revenue produced by an investment will be K(t) thousand dollars per year at time t, where K(t) = 9te^{-0.2t}. Find the present value of this stream of income over the next four years using 10% interest rate.

Enter just an integer (no units) representing the amount to the nearest dollar.

38) A large conglomerate estimates that a new plant will yield an annual rate of return of 5000 - 250t thousand dollars. If the interest rate is 9%, what is the present value of the income generated in the first three years of the plant's operation?

Enter just an integer (no units) representing the amount to the nearest dollar.

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

Solve the problem.

39) An investment is expected to produce a uniform continuous rate of money flow of $500 per year for 10 years. Find the present value at 5% compounded continuously.

A) $3934.69

B) $6487.21

C) $16,065.31

D) $6065.31

40) The rate of acontinuous money flow is 500e^{0.04} dollars per year for 10 years. Find the present value if interest is earned at 7% compounded continuously.

A) $5830.98

B) $29,013.64

C) $22,497.65

D) $4319.70

41) The rate of acontinuous money flow is 1000e^{-0.4} dollars per year for 10 years. Find the present value if interest is earned at 5% compounded continuously.

A) $16,217.81

B) $6593.67

C) $27,328.92

D) $15,628.55

42) A money market fund has acontinuous flow of money at a rate of 0.01x + 900 dollars for 10 years. Find the present value of this flow if interest is earned at 6% compounded continuously.

A) $23,237.39

B) $5206.28

C) $5640.14

D) $6768.16

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

43) In 1940, the population density of Philadelphia was given by 60e^{-0.4t} thousand people per square mile at a distance t miles from City Hall. How many people lived between 1 and 3 miles from City Hall?

Enter just an integer (no words) representing the number to the nearest thousand.

44) Determine whether the expressions approach a limit as b→∞. If they do, give the value of the limit. b(b + 3)^{-2}, (2√(b) - 1/√(b)), e^{3b} + 2

Enter your answer as just a, b, c where these are either limits (integers) or the words "no limit" in the same order they appear above separated by commas.