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 relationship between weight and systolic blood pressure in children. Using hospital records for 5,000 children, the experimenters found that the systolic blood pressure was given approximately by P(x) = 17.511 + ln x2 10 ≤ x ≤ 100 where P1x2 is measured in millimeters of mercury and x is measured in pounds. What is the rate of change of blood pressure with respect to weight at the 40-pound weight level? At the 90-pound weight level?
> Find each indicated derivative and simplify.
> An experiment consists of tossing three fair (not weighted) coins, except those one of the three coins has a head on both sides. Compute the probability of obtaining the indicated results. 0 Heads
> Find each indicated derivative and simplify.
> Find each indicated derivative and simplify.
> Find each indicated derivative and simplify.
> Find each indicated derivative and simplify.
> Find ′(x) in two ways: (1) using the product or quotient rule and (2) simplifying first.
> Find ′(x) in two ways: (1) using the product or quotient rule and (2) simplifying first.
> Find ′ (x) and find the value(s) of x where ′ (x) = 0.
> Find ′ (x) and find the value(s) of x where ′ (x) = 0.
> Find  (x) and find the equation of the line tangent to the graph of  at x = 2.
> Find  (x) and find the equation of the line tangent to the graph of  at x = 2.
> (A) What are the odds for rolling a sum of 10 in a single roll of two fair dice? (B) If you bet $1 that a sum of 10 will turn up, what should the house pay (plus returning your $1 bet) if a sum of 10 turns up in order for the game to be fair? A pair of
> Find  (x) and find the equation of the line tangent to the graph of  at x = 2.
> (A) Find (x) using the quotient rule, and (B) Explain how (x) can be found easily without using the quotient rule.
> (A) Find (x) using the quotient rule, and (B) Explain how (x) can be found easily without using the quotient rule.
> Find the indicated derivatives and simplify.
> find the indicated derivatives and simplify.
> find the indicated derivatives and simplify.
> Find the indicated derivatives and simplify.
> Find the indicated derivatives and simplify.
> Find h′(x), where (x) is an unspecified differentiable function.
> Find h′(x), where (x) is an unspecified differentiable function.
> An experiment consists of tossing three fair (not weighted) coins, except those one of the three coins has a head on both sides. Compute the probability of obtaining the indicated results. 2 Heads
> Find h′(x), where (x) is an unspecified differentiable function.
> Find h′(x), where (x) is an unspecified differentiable function.
> Find h′(x), where (x) is an unspecified differentiable function.
> Find h′(x), where (x) is an unspecified differentiable function.
> Find (x) and simplify.
> Find (x) and simplify.
> Find (x) and simplify.
> Find (x) and simplify.
> Find (x) and simplify.
> Find (x) and simplify.
> Compute the odds against obtaining. An odd number or a number divisible by 3 in a single roll of a die.
> Find (x) and simplify.
> Find (x) and simplify.
> Find (x) and simplify.
> Find (x) and simplify.
> Find (x) and simplify.
> Find (x) and simplify.
> Find (x) and simplify.
> Find (A) the derivative of T(x) / B(x) without using the quotient rule, and (B) T′(x) / B′(x). Note that the answer to part (B) is different from the answer to part (A).
> solve for the variable without using a calculator. ln x = 2
> solve for the variable without using a calculator. log10 x = -3
> 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 without using a calculator. y = log4 64
> An investment of $25,000 earns interest at an annual rate of 8.4% compounded continuously. (A) Find the instantaneous rate of change of the amount in the account after 2 years. (B) Find the instantaneous rate of change of the amount in the account at t
> A mathematical model for the average of a group of people learning to type is given by N(t) = 10 + 6 ln t t ≥ 1 where N(t) is the number of words per minute typed after t hours of instruction and practice (2 hours per day, 5 days per week). What is t
> 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?
> 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?
> 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
