A note will pay $50,000 at maturity 5 years from now. How much should you be willing to pay for the note now if money is worth 6.4% compounded continuously?
> Blood pressure. Refer to Problem 71. Find the weight (to the nearest pound) at which the rate of change of blood pressure with respect to weight is 0.3 millimeter of mercury per pound. Data from Problem 71: An experiment was set up to find a relationshi
> Repeat Problem 69 for a starting colony of 1,000 bacteria such that a single bacterium divides every 0.25 hour. Data from Problem 69: A single cholera bacterium divides every 0.5 hour to produce two complete cholera bacteria. If we start with a colony o
> The estimated resale value R (in dollars) of a company car after t years is given by R (t) = 20,000(0.86)t What is the rate of depreciation (in dollars per year) after 1 year? 2 years? 3 years?
> Use the result of Problem 65 and the four-step process to show that if (x)= ecx, then (x)= cecx.
> use graphical approximation methods to find the points of intersection of (x) and g(x) (to two decimal places).
> use graphical approximation methods to find the points of intersection of (x) and g(x) (to two decimal places).
> use graphical approximation methods to find the points of intersection of (x) and g(x) (to two decimal places). [Note that there are two points of intersection and that ex is greater than x5 for large values of x.]
> Compute the odds against obtaining. 2 heads when a single coin is tossed twice.
> find dy/dx for the indicated function y. y = e3 - 3x
> find dy/dx for the indicated function y. y = -log2 x + 10 ln x
> find dy/dx for the indicated function y. y = x5 - 5x
> find dy/dx for the indicated function y. y = log x + 4x2 + 1
> find dy/dx for the indicated function y. y = 4x
> find dy/dx for the indicated function y. y = 3 log5 x
> first use appropriate properties of logarithms to rewrite (x), and then find (x).
> first use appropriate properties of logarithms to rewrite (x), and then find (x).
> Refer to Problem 41. Does the line tangent to the graph of (x) = ln x at x = e pass through the origin? Are there any other lines tangent to the graph of f that pass through the origin? Explain. A student claims that the line tangent
> Refer to Problem 39. Does the line tangent to the graph of (x)= ex at x = 1 pass through the origin? Are there any other lines tangent to the graph of f that pass through the origin? Explain. Data from Problem 39: A student claims th
> An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 2 (page 398) and, assuming each simple event is as likely as any other, find the probability of the sum of the dots ind
> Find the equation of the line tangent to the graph of  at the indicated value of x.
> Find the equation of the line tangent to the graph of  at the indicated value of x.
> Find the equation of the line tangent to the graph of  at the indicated value of x.
> Find the equation of the line tangent to the graph of  at the indicated value of x.
> find ′(x).
> find ′(x).
> find ′(x).
> find ′(x).
> find ′(x).
> find ′(x).
> Compute the odds in favor of obtaining. 1 head when a single coin is tossed twice.
> find ′(x).
> find ′(x).
> find ′(x).
> use logarithmic properties to write in simpler form.
> use logarithmic properties to write in simpler form. ln xy
> use logarithmic properties to write in simpler form. ln ex
> solve for the variable to two decimal places. 50,000 = Pe0.054(7)
> solve for the variable to two decimal places. A = 3,000e0.071102
> Some developed nations have population doubling times of 200 years. At what continuous compound rate is the population growing? (Use the population growth model in Problem 47.) Data from Problem 47: A mathematical model for world population growth over
> How long will it take for the U.S. population to double if it continues to grow at a rate of 0.78% per year
> An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 2 (page 398) and, assuming each simple event is as likely as any other, find the probability of the sum of the dots ind
> A strontium isotope has a half-life of 90 years. What is the continuous compound rate of decay? (Use the radioactive decay model in Problem 43.) Data from Problem 43: A mathematical model for the decay of radioactive substances is given by Q = Q0ert wh
> The continuous compound rate of decay of carbon-14 per year is r = -0.000 123 8. How long will it take a certain amount of carbon-14 to decay to half the original amount? (Use the radioactive decay model in Problem 43.) Data from Problem 43: A mathemati
> (A) Show that the rate r that doubles an investment at continuously compounded interest in t years is given by (B) Graph the doubling-rate equation from part (A) for 1 ≤ t ≤ 20. Is this restriction on t reasonabl
> A woman invests $5,000 in an account that earns 8.8% compounded continuously and $7,000 in an account that earns 9.6% compounded annually. Use graphical approximation methods to determine how long it will take for her total investment in the two accounts
> At what nominal rate compounded continuously must money be invested to double in 10 years?
> How long will it take money to double if it is invested at 5% compounded continuously?
> Referring to Problem 33, in how many years will the $10,000 be due in order for its present value to be $5,000? Data from Problem 33: Solving A = Pert for P, we obtain P = Ae-rt which is the present value of the amount A due in t years if money earns in
> A family paid $99,000 cash for a house. Fifteen years later, the house was sold for $195,000. If interest is compounded continuously, what annual nominal rate of interest did the original $99,000 investment earn?
> Provident Bank also offers a 3-year CD that earns 1.64% compounded continuously. (A) If $10,000 is invested in this CD, how much will it be worth in 3 years? (B) How long will it take for the account to be worth $11,000?
> Compute the odds in favor of obtaining. A number divisible by 3 in a single roll of a die
> Without using a calculator, determine which event, E or F, is more likely to occur.
> It can be shown that for any real number s. Illustrate this equation graphically for s = 2 by graphing in the same viewing window, for 1 ≤ n ≤ 50.
> Use a calculator and a table of values to investigate Do you think this limit exists? If so, what do you think it is?
> use a calculator to complete each table to five decimal places.
> solve for t or r to two decimal places. 3 = e20r
> solve for t or r to two decimal places. 3 = e0.08t
> solve for t or r to two decimal places. 2 = e18r
> solve for t or r to two decimal places. 2 = e0.09t
> If $4,000 is invested at 8% compounded continuously, graph the amount in the account as a function of time for a period of 6 years.
> Use a calculator to evaluate A to the nearest cent A = $10,000e0.1t for t = 10, 20, and 30
> solve for the variable to two decimal places. 4,840 = 3,750e4.25r
> An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 2 (page 398) and, assuming each simple event is as likely as any other, find the probability of the sum of the dots ind
> solve for the variable to two decimal places. 10,000 = 7,500e0.085t
> let C(x) = 10,000 + 150x - 0.2x2 be the total cost in dollars of producing x bicycles Find the cost of producing the 200th bicycle.
> let C(x) = 10,000 + 150x - 0.2x2 be the total cost in dollars of producing x bicycles Find the total cost of producing 199 bicycles.
> let C(x) = 10,000 + 150x - 0.2x2 be the total cost in dollars of producing x bicycles Find the total cost of producing 100 bicycles.
> Table 2 contains price–demand and total cost data for the production of treadmills, where p is the wholesale price (in dollars) of a treadmill for an annual demand of x treadmills and C is the total cost (in dollars) of producing x tre
> The price–demand equation and the cost function for the production of handwoven silk scarves are given, respectively, by p = 60 - 21x and C(x)= 3,000 + 5x where x is the number of scarves that can be sold at a price of $p per unit and C(x) is the total
> The total cost and the total revenue (in dollars) for the production and sale of x hair dryers are given, respectively, by (A) Find the value of x where the graph of R(x) has a horizontal tangent line. (B) Find the profit function P(x). (C) Find the
> The company in Problem 47 is also planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are a weekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a pr
> The price–demand equation and the cost function for the production of HDTVs are given, respectively, by x = 9,000 - 30p and C(x) = 150,000 + 30x where x is the number of HDTVs that can be sold at a price of $p per TV and C(x) is the total cost (in dolla
> The price p (in dollars) and the demand x for a particular steam iron are related by the equation x = 1,000 - 20p (A) Express the price p in terms of the demand x, and find the domain of this function. (B) Find the revenue R(x) from the sale of x steam
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If E and F are mutually exclusive events, then E and F are complementary.
> The total profit (in dollars) from the sale of x gas grills is P(x) = 20x - 0.02x2 - 320 0 ≤ x ≤ 1,000 (A) Find the average profit per grill if 40 grills are produced. (B) Find the marginal average profit at a production level of 40 grills and interp
> The total profit (in dollars) from the sale of x cameras is P(x) = 12x - 0.02x2 - 1,000 0 ≤ x ≤ 600 Evaluate the marginal profit at the given values of x, and interpret the results. (A) x = 200 (B) x = 350
> The total profit (in dollars) from the sale of x calendars is P(x) = 22x - 0.2x2 - 400 0 ≤ x ≤ 100 (A) Find the exact profit from the sale of the 41st calendar. (B) Use the marginal profit to approximate the profit from the sale of the 41st calendar.
> The total cost (in dollars) of printing x board games is C(x) = 10,000 + 20x (A) Find the average cost per unit if 1,000 board games are produced. (B) Find the marginal average cost at a production level of 1,000 units and interpret the results. (C) U
> The total cost (in dollars) of producing x electric guitars is C(x) = 1,000 + 100x - 0.25x2 (A) Find the exact cost of producing the 51st guitar. (B) Use marginal cost to approximate the cost of producing the 51st guitar.
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. Marginal average cost is equal to average marginal cost.
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a price–demand equation is linear, then the marginal revenue function is linear.
> find the indicated function if cost and revenue are given by C(x) = 145 + 1.1x and R(x) = 5x - 0.02x2 , respectively. Marginal average Profit function
> find the indicated function if cost and revenue are given by C(x) = 145 + 1.1x and R(x) = 5x - 0.02x2 , respectively. Marginal Profit function
> find the indicated function if cost and revenue are given by C(x) = 145 + 1.1x and R(x) = 5x - 0.02x2 , respectively. Marginal average revenue function
> An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 2 (page 398) and, assuming each simple event is as likely as any other, find the probability of the sum of the dots ind
> find the indicated function if cost and revenue are given by C(x) = 145 + 1.1x and R(x) = 5x - 0.02x2 , respectively. Average revenue function
> find the marginal profit function if the cost and revenue, respectively, are those in the indicated problems. Problem 12 and Problem 16 Data from Problem 12 and Problem 16:
> find the marginal profit function if the cost and revenue, respectively, are those in the indicated problems. Problem 10 and Problem 14 Data from Problem 10 and Problem 14:
> find the marginal revenue function.
> find the marginal revenue function.
> find the marginal cost function. C(x ) = 640 + 12x - 0.1x2
> find the marginal cost function. C(x ) = 2,700 + 6x
> let C(x) = 10,000 + 150x - 0.2x2 be the total cost in dollars of producing x bicycles Find the average cost per bicycle of producing 200 bicycles.
> let g(x) = x2 and find the given values without using a calculator
> let  (x) = 0.1x + 3 and find the given values without using a calculator
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The theoretical probability of an event is less than or equal to its empirical probability.
> let  (x) = 0.1x + 3 and find the given values without using a calculator
> If a person learns y items in x hours, as given approximately by what is the approximate increase in the number of items learned when x changes from 1 to 1.1 hours? From 4 to 4.1Â hours?
> One hour after x milligrams of a particular drug are given to a person, the change in body temperature T (in degrees Fahrenheit) is given by Approximate the changes in body temperature produced by the following changes in drug dosages: (A) From 2 to 2.
> An egg of a particular bird is nearly spherical. If the radius to the inside of the shell is 5 millimeters and the radius to the outside of the shell is 5.3 millimeters, approximately what is the volume of the shell? Remember that:
