4. t 1. a) c) = 2. MATH 5: DERIVATIVE WORKSHEET (2.4) Find the derivative y' of each by Chain Rule: y = (3x³ - 2)² a) b) y = (2x³ −3x² +1)* Cable TV Subscribers: The number of subscribers of CNC Cable Television in the town of Randolph is approximated by the function: N(x) = 1000√1+2x (1≤x≤ 30) where N(x) denotes the number of subscribers to the service in the xth week. Find the rate of increase in the number of subscribers at the end of the 12th week. a) b) 3. Cost of Wireless Phone Calls: As cellular phone usage continues to soar, the airtime costs have dropped. The average price per minute of use (in cents) is projected to be f(t) = 31.88(1 + t) (0≤t≤6) where t is measured in years and t = 0 corresponds to the beginning of 1998. What was the average price/minute of use at the beginning of 2000? Compute f'(t) How fast was the average price/minute of use changing at the beginning of 2000? Male Life Expectancy: Suppose the life expectancy of a male at birth in a certain country is descri
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12. The linear function f(x) = -9.8x + 24 models the percentage of people, f(x), who eat at fast food restaurants each week x years after 2009. What is the slope and what does it mean? m = -9.8; the percentage of people eating at fast food restaurants each week has decreased at a rate of 9.8% per year after 2009. 13. The function f(t) = -0.12t^2 + 0.53t + 30.8 models the U.S population in millions, ages 65 and older, where t represents years after 1990. The function g(t) = 0.55t^2 + 11.89t + 105.3 models the total yearly cost of Medicare in billions of dollars, where t represents years after 1990. What does the function gf represent? Find gf(15) Cost per person in thousands of dollars: $34.67 thousand
Adi S.
7. Find a formula for h'(x) when: (a) h(x) = f(x^2); and (b) h(x) = f(x^n g(x)). 8. Let s(t) be the distance in kilometres a car goes in t hours. Let B(s) be the number of lit fuel the car uses to go s kilometres. Provide an interpretation of the function b(t) = B(s(t)) find a formula for b'(t). 9. Suppose that C = 20q - 4q (25 - 1/2 x)^1/2, where q is a constant and x < 50. Find dC/dx. 10. Differentiate each of the following in two different ways: (a) y = (x^4)^5 = x^20 (b) y = (1 - x)^3 = 1 - 3x + 3x^2 - x^3 11. Suppose you invest ‑1 000 at p% interest per year. Let g(p) denote how many euros yo have after ten years. (a) Give economic interpretations of: (i) g(5) ≈ 1629; and (ii) g'(5) ≈ 155. (b) To check the numbers in (a), find a formula for g(p), then compute g(5) and g'(5). 12. If f is differentiable at x, find expressions for the derivatives of the following functions: (a) x + f(x) (b) [f(x)]^2 - x (c) [f(x)]^4 (d) x^2 f(x) + [f(x)]^3
Vincenzo Z.
A store finds that its sales revenue changes at a rate given by S'(t) = -30t^2 + 380t dollars per day, where t is the number of days after an advertising campaign ends and 0 ≤ t ≤ 30. (a) Find the total sales for the first week after the campaign ends (t = 0 to t = 7). (b) Find the total sales for the second week after the campaign ends (t = 7 to t = 14). The income from an oil change service chain can be considered as flowing continuously at an annual rate given by f(t) = 30,000e^(0.04t) (dollars/year). Find the total income for this chain over the first 2 years (from t = 0 to t = 2). (Round your answer to the nearest cent.)
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