Refer to Problem 63. Light intensity I relative to depth d (in feet) for one of the clearest bodies of water in the world, the Sargasso Sea, can be approximated by I = I0e - 0.00942d where I0 is the intensity of light at the surface. What percentage of the surface light will reach a depth of (A) 50 feet? (B) 100 feet? Data from Problem 63: Marine life depends on the microscopic plant life that exists in the photic zone, a zone that goes to a depth where only 1% of surface light remains. In some waters with a great deal of sediment, the photic zone may go down only 15 to 20 feet. In some murky harbors, the intensity of light d feet below the surface is given approximately by I = I0e - 0.23d where I0 is the intensity of light at the surface. What percentage of the surface light will reach a depth of (A) 10 feet? (B) 20 feet?
> In its first 10 years the Janus Flexible Income Fund produced an average annual return of 9.58%. Assume that money invested in this fund continues to earn 9.58% compounded annually. How long (to the nearest year) will it take money invested in this fund
> Let p(x) = log x, q(x) and r(x) = x. Use a graphing calculator to draw graphs of all three functions in the same viewing window for 1 ( x ( 16. Discuss what it means for one function to be smaller than another on an interval, and then order the three fu
> Sketch a graph of each equation or pair of equations in a rectangular coordinate system. 5x - 6y = 15
> Explain why 1 is not a suitable logarithmic base.
> Graph using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals. Y = 4 ln (x-3)
> Graph using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals. Y = 2 ln x + 2
> Graph using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals. y = ln |x|
> Graph using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals. y = - ln x
> Solve each equation to four decimal places. 1.024t = 2
> Solve each equation to four decimal places ex = 0.3059
> Solve each equation to four decimal places. 10x = 153
> Find x to four decimal places. (A) log x = 2.0832 (B) log x = -1.1577 (C) ln x = 3.1336 (D) ln x = -4.3281
> Evaluate to five decimal places using a calculator. (A) log 72.604 (B) log 0.033 041 (C) ln 40,257 (D) ln 0.005 926 3
> Find the solution set.
> What are the domain and range of the function defined by y = log (x – 1) - 1?
> Explain how the graph of the equation in Problem 56 can be obtained from the graph of y = log 3 x using a simple trans formation (see Section 2.2). Data From Problem 56:
> Graph the Problems by converting to exponential form first.
> Find x
> Find x
> Find x
> discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If g is the inverse of a function , then is the inverse of g.
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The inverse of:
> discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The graph of a one-to-one function intersects each vertical line exactly once
> Sketch a graph of each equation or pair of equations in a rectangular coordinate system.
> solve for x 31x + 62 = 5 - 21x + 12
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. Every polynomial function of odd degree is one-to-one.
> Find x, y, or b without using a calculator.
> Find x, y, or b without using a calculator.
> Find x, y, or b without using a calculator.
> Find x, y, or b without using a calculator.
> Find x, y, or b without using a calculator.
> Write in simpler form,
> Write in simpler form,
> Write in simpler form,
> Evaluate the expression without using a calculator.
> Find the solution set.
> Evaluate the expression without using a calculator.
> Evaluate the expression without using a calculator.
> Evaluate the expression without using a calculator.
> Evaluate the expression without using a calculator.
> Rewrite in equivalent logarithmic form.
> Rewrite in equivalent logarithmic form.
> Graph each function in over the indicated interval.
> Graph each function in over the indicated interval.
> Graph each function in over the indicated interval.
> Match each equation with the graph of f, g, h, or k in the figure. (A) y = (¼) x (B) y = (0.5) x (C) y = 5x (D) y = 3x
> Use the graph of each line to find the x intercept, y intercept, and slope. Write the slope-intercept form of the equation of the line.
> From the dawn of humanity to 1830, world population grew to one billion people. In 100 more years (by 1930) it grew to two billion, and 3 billion more were added in only 60 years (by 1990). In 2016, the estimated world population was 7.4 billion with a r
> In 2015, the estimated population of Brazil was 204 million with a relative growth rate of 0.77%. (A) Write an equation that models the population growth in Brazil, letting 2015 be year 0. (B) Based on the model, what is the expected population of Brazi
> Table 5 shows estimates of mobile data traffic, in exabytes 11018 bytes2 per month, for years from 2015 to 2020. (A) Let x represent the number of years since 2015 and find an exponential regression model (y = abx ) for mobile data traffic. (B) Use the
> People assigned to assemble circuit boards for a computer manufacturing company undergo on-the-job training. From past experience, the learning curve for the average employee is given by N = 40 ( 1 - e - 0.12t ) where N is the number of boards assem
> Refer to Problem 57. The following rates for 60-month certificates of deposit were also taken from BanxQuote websites: (A) Oriental Bank & Trust, 1.35% compounded quarterly (B) BMW Bank of North America, 1.30% compounded monthly (C) BankFirst Corporat
> A couple just had a baby. How much should they invest now at 5.5% compounded daily in order to have $40,000 for the child’s education 17 years from now? Compute the answer to the nearest dollar.
> Suppose that $4,000 is invested at 6% compounded weekly. How much money will be in the account in (A) ½ year? (B) 10 years? Compute answers to the nearest cent.
> Find the value of an investment of $24,000 in 7 years if it earns an annual rate of 4.35% compounded continuously.
> Graph each function over the indicated interval.
> Find the Solution Set x - 2 ≥ 2(x – 5)
> Graph each function over the indicated interval.
> Solve each equation for x. (Remember: ex ( 0 and e - x ( 0 for all values of x).
> Solve each equation for x. (Remember: ex ( 0 and e - x ( 0 for all values of x).
> Solve each equation for x. (Remember: ex ( 0 and e - x ( 0 for all values of x).
> Solve each equation for x. (Remember: ex ( 0 and e - x ( 0 for all values of x).
> Solve each equation for x.
> Solve each equation for x.
> Solve each equation for x.
> Solve each equation for x.
> Solve each equation for x.
> Use the graph of each line to find the x intercept, y intercept, and slope. Write the slope-intercept form of the equation of the line.
> Find real numbers a and b such that a ( b but a4 = b4. Explain why this does not violate the third exponential function property in Theorem 2 on page 98.
> Graph each function over the indicated interval.
> Graph each function over the indicated interval.
> Graph each function over the indicated interval.
> Use the graph of ( shown in the figure to sketch the graph of each of the following. (A) y = ((x) + 2 (B) y = ((x – 3) (C) y = 2 ((x) - 4 (D) y = 4 - ((x + 2)
> describe verbally the transformations that C can be used to obtain the graph of g from the graph of ((see Section 2.2).
> describe verbally the transformations that C can be used to obtain the graph of g from the graph of f (see Section 2.2).
> describe verbally the transformations that C can be used to obtain the graph of g from the graph of f (see Section 2.2).
> describe verbally the transformations that C can be used to obtain the graph of g from the graph of f (see Section 2.2).
> Graph each function in over the indicated interval.
> Find the Solution Set -314 - x2 = 5 - 1x + 12
> For each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercepts ((x) = (x – 5)2 (x + 7)2
> For each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercepts ((x) = 5x6 + x4 + 4x8 + 10
> For each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercepts ((x) = 30 - 3x
> For each polynomial function find the following: (A) Degree of the polynomial (B) All x intercepts (C) The y intercepts ((x) = x2 - 5x + 6
> Refer to Table 5. (A) Let x represent the number of years since 1960 and find a cubic regression polynomial for the divorce rate. (B) Use the polynomial model from part (A) to estimate the divorce rate (to one decimal place) for 2025.
> n 1917, L. L. Thurstone, a pioneer in quantitative learning theory, proposed the rational function to model the number of successful acts per unit time that a person could accomplish after x practice sessions. Suppose that for a particular person enroll
> Refer to Table 4. (A) Let x represent the number of years since 2000 and find a cubic regression polynomial for the per capita consumption of eggs. (B) Use the polynomial model from part (A) to estimate (to the nearest integer) the per capi
> The financial department of a hospital, using statistical methods, arrived at the cost equation C(x) = 20x3 - 360x2 + 2,300x - 1,000 1 ( x ( 12 where C(x) is the cost in thousands of dollars for handling x thousand cases per month. The average cost per
> Financial analysts in a company that manufactures DVD players arrived at the following daily cost equation for manufacturing x DVD players per day: C(x) = x2 + 2x + 2,000 The average cost per unit at a production level of x players per day is C(x) = C(x
> A company manufacturing surfboard has fixed costs of $300 per day and total costs of $5,100 per day at a daily output of 20 boards. (A) Assuming that the total cost per day, C(x), is linearly related to the total output per day, x, write an equation for
> Write an equation of the line with the indicated slope and y intercept.
> Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure.
> Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure.
> For each rational function, (A) Find any intercepts for the graph. (B) Find any vertical and horizontal asymptotes for the graph. (C) Sketch any asymptotes as dashed lines. Then sketch a graph of f. (D) Graph the function in a standard viewing window
> For each rational function, (A) Find any intercepts for the graph. (B) Find any vertical and horizontal asymptotes for the graph. (C) Sketch any asymptotes as dashed lines. Then sketch a graph of f. (D) Graph the function in a standard viewing window
> For each rational function, (A) Find any intercepts for the graph. (B) Find any vertical and horizontal asymptotes for the graph. (C) Sketch any asymptotes as dashed lines. Then sketch a graph of f. (D) Graph the function in a standard viewing window
> Find the equations of any vertical asymptotes.
> Find the equations of any vertical asymptotes.
> Find the equations of any vertical asymptotes.
> Find the equation of any horizontal asymptote.
> Find the equation of any horizontal asymptote.
