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Consider the functions in Exercises 5–8 as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days. Find the average rates of change of
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Finite Mathematics and Applied Calculus (MindTap Course List)
- The following table shows total military and arms trade expenditure for a certain country in 2000, 2006, and 2012. Year t (year since 2000) 0 6 12 Military Expenditure C(t)($ billion) 390 550 640 (a) Compute the average rate of change of C(t) over the period 2006–2012 (that is, [6, 12]). Be sure to state the units of measurement. HINT [See Example 1.] Interpret the average rate of change. This country's military expenditure increased at an average rate of about between 2006 and 2012. (b) Compute the average rate of change of C(t) over the period [0, 12]. Be sure to state the units of measurement. HINT [See Example 1.] (Round your answer to two decimal places.) Interpret the average rate of change. (Round your answer to two decimal places.) This country's military expenditure increased at an average rate of about between 2000 and 2012.arrow_forwardFind the derivatives of the functions in Exercises 17–40. 20. f(t) t? + t – 2arrow_forwardSuppose that during the period 1990–2001, U.S. imports of pasta increased from 300 million pounds in 1990 (t = 0) by an average of 35 million pounds/year. (a) Use these data to express q, the annual U.S. imports of pasta (in millions of pounds), as a linear function of t, the number of years since 1990. q(t) = (b)Use your model to estimate U.S. pasta imports (in millions of pounds) in 2006, assuming the import trend continued. _________million poundsarrow_forward
- Suppose that during the period 1990–2001, U.S. imports of pasta increased from 270 million pounds in 1990 (t = 0) by an average of 50 million pounds/year. (a) Use these data to express q, the annual U.S. imports of pasta (in millions of pounds), as a linear function of t, the number of years since 1990. q(t) = (b) Use your model to estimate U.S. pasta imports (in millions of pounds) in 2003, assuming the import trend continued.arrow_forwardUse a CAS to perform the following steps in Exercises 59–60. a. Plot the equation with the implicit plotter of a CAS. Check to see that the given point P satisfies the equation. b. Using implicit differentiation, find a formula for the derivative dy/dx and evaluate it at the given point P. c. Use the slope found in part (b) to find an equation for the tangent line to the curve at P. Then plot the implicit curve and tangent line together on a single graph. 59. x3 - xy + y3 = 7, P (2, 1) 60. x5 + y3x + yx2 + y4 = 4, P (1,1)arrow_forwardFind the maximum rate of change of f at the given point and the direction in which it occurs.arrow_forward
- Exercises 99–102: Compute the average rate of change of f from x, to x2. Round your answer to two decimal places when appropriate. 101. f (x) = /2x – 1, x1 = 1, and x2 = 3 - %3D %3Darrow_forwardFind the linearization of the function at x = a = -4arrow_forwardThe graph shows the depth of water W in a reservoir over a one-year period as a function of the number of days x since the beginning of the year. What was the average rate of change of W between x = 0 and x = 300? (Assume that the points lie on the grid lines.)arrow_forward
- a) Find the demand as a function of time t. b) Find the rate of change of the quantity demanded when t=80 days.arrow_forwardA tractor has an initial price of $8000.00 and sells for $1100.00 after 23 years. Assume that the tractor's value depreciates linearly with the passing years. (a) Let V represent the tractor's value in dollars and let t represent the number of years since the tractor was purchased. Write a formula to express the tractor's value as a function of time: V(t) = ... ... (b) Horizontal intercept of the value function V(t): ... Vertical intercept of the value function V(t):arrow_forwardFish enter a lake at a rate modeled by the function Earrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage