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Problems 65–72, use a graphing calculator to graph the given examples of the various cases in Table 1 on page 354.
66. Unlimited growth:
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- . Subprime Mortgage Debt during the Housing Bubble (Compare Exercise 104.) During the real estate run-up 2000–2008 the value of subprime (normally classified as risky) mortgage debt outstanding in the United States could be approximated by in 1,350 A(t) = 1 + 4.2(1.7) billion dollars (0arrow_forwardIn Problems 61–74, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. 61. logs(x + 1) – log4(x – 2) = 1 62. log2 (x – 1) – log6(x + 2) = 2 63. e* = -x 64. e2* = x + 2 65. e* = x² 66. e* = x 69. In x = x – 1 73. e* = In x 67. In x = -x 68. In (2x) = -x + 2 70. In x = -x? 71. e + In x = 4 72. e - In xr = 4 74. e = -In xarrow_forwardAccording to the U.S. Customs and Border Protection Agency, the average airport wait time at Chicago’sO’Hare International airport is 16 minutes for a traveler arrivingduring the hours 7–8 a.m., and 32 minutes for arrival during thehours 4–5 p.m. The wait time is defined as the total processingtime from arrival at the airport until the completion of a passenger’s security screening. Assume the wait time is exponentiallydistributed.a. What is the probability of waiting between 10 and 30 minutesfor a traveler arriving during the 7–8 a.m. hour?b. What is the probability of waiting more than 25 minutes for atraveler arriving during the 7–8 p.m. hour?arrow_forward3. Determine the exponential function that passes through the points ( 2, 8) and (-1 1) (3 pts) Chparrow_forward3. Find the formula for the exponential function passing through the points (0,1.5) and (1,5).arrow_forward1 Suppose that $78,000 is invested at 4,% interest, compounded quarterly. 2 a) Find the function for the amount to which the investment grows after t years. b) Graph the function. c) Find the amount of money in the account at t= 0, 3, 5, and 10 years. d) When will the amount of money in the account reach $300,000? a) The function for the amount to which the investment grows after t years is A()3D (Simplify your answer. Type an expression using t as the variable.)arrow_forward3. Once an antibiotic is introduced to bacteria, the number of bacteria decreases exponentially. For example, beginning with 1 million bacteria, the amount present t days from the time streptomycin is introduced is given by the function A(t) = 1,000,000(2)-t/10. Rounding to the nearest thousand, determine how many bacteria are present after 1 week.arrow_forwardQuestion 5 In 1999, the population of Richmond-Petersburg, Virginia, metropolitan area, was 961,400 and was increasing at a at roughly 9200 people per year. The average annual income in the area was $30,593 per capita, and this average was increasing at about $1400 per year. Use the product rule to estimate the rate at which total personal income was rising in the area at this time. Explain the meaning of each term in the product rule. Question 6 Use Logarithmic differentiation to prove the product rule and the quotient rule. Hint: Let f(x) = A(x)B(x) and g(x) = C(x)/D(x) to start then take the natural log of both sides of each equation and then take the derivative of both sides of the equation. Question 7 Use Logarithmic differentiation to find the derivative of a" for a positive constant a.arrow_forward2.A mold population is growth at 8% every three months. If there is initially 3 cubic centimeters of mold, when will the mold have grown to 10 cubic centimeters?arrow_forwardUse the Jesaki Inc Information Below to Solve Questions 1- Below 1) Jesaki Inc estimates that it will sell N(x) units of product after spending $x thousand on advertising, as given by N(x) = -0.45 x^4 + 46 x^3 1,079 x x^2+ 161,973. What is the point of diminishing returns? Round to the nearest dollar. 2) The number x of bicycle helmets Jesaki Inc is willing to sell per week at a price of $p is given by x = a/p + b-c, where a = 80, b = 26, and c = 414. Find the instantaneous rate of change of the supply with respect to price when the price is $79. Round to the nearest hundredth (2 decimal places). 3) Jesaki Inc sponsered a blood drive following mathematical model relating systolic blood pressure and age: P(x) = a + bln(x+1), where P(x) is pressure, measured in millimeters of mercury, and x is age in years. By examining Guilford County hospital records, they estimate the values for Guilford County to be a = 43 and b = 27. Using this model, estimate the rate of change of pressure with…arrow_forward11. Find the equation of the exponential function given below graphically in the form y = a · 2* + b. -3-arrow_forward4.3.101 Suppose that $2000 is invested in an account that pays interest compounded continuously. Find the amount of time that it would take for the account to grow to $4500 at 5.25%. It would take approximately || years. (Round to the nearest tenth.)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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