1. The function S(t) (where t is measured in weeks starting with t = 0) approximates thestock prices of AAPL between 2/20 and 3/20. We know thatFind S(t) and compute the average stock price over the period 2/20-3/20 using aleft-Riemann sum with a partition into 4 subintervals of equal width.160158156154152150148146S" (t) = −46.8+55.2t - 13.08²,S(0) = 146.7,S'(0) = 19.6.AAPL Stock PricesS(t)2023-02-202023-02-272023-03-062023-03-132023-03-20Figure 1: AAPL Stock Prices 2/20-3/20.

Answered: 1. The function S(t) (where t is…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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4) The data below shows N = f(t), the number of Facebook subscribers, in millions, worldwide at 3-month intervals for one calendar year. Month, t Mar. Jun. Sep. Dec. Mar. 2011 2011 2011 2011 2012 664.0 710.7 756.9 799.1 835.5 a) Calculate the average rate of change of N per month for the time intervals shown. Are these the values f'(t)? If not, how close are they? b) What can you say about the sign of d²n/dt? for the 12-month period between March, 2011 and March, 2012? (Hint: Calculate a few values of the second derivative using your values from part a). Alternatively, a graph may make the answer obvious.)
2. An investment of $100 is placed into an account that earns interest, compounded annually, at a rate of 5% for 7 years. The amount, A, in the account can be modelled by the function A = 100(1.05)', where t is the time, in years. What is the domain of this function? a. (t e R, 2 7} b. (t e R, 0 SIS7) c. (te R, t > 7} d. (t e R,0
Suppose that a continuous income stream has an annual rate of flow f(t) = 500e−0.02t2 (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income (in dollars) from this stream over the next 4 years. (Round your answer to the nearest dollar.)
K An automobile company is ready to introduce a new line of cars through a national sales campaign. After test marketing the line in a carefully selected city, the marketing research department estimates that the sales (in millions of dollars) will increase at the monthly rate of the following function for t months after the campaign has started. S'(t) = 16-14e-0.1t Osts23 (A) What will be the total sales, S(t), t months after the beginning of the national sales campaign if we assume no sales at the beginning of the campaign? -0.11-140 S(t)= 16t+140e (B) What are the estimated total sales for the first 11 months of the campaign? 83 million. (Round to the nearest whole number.) (C) When will the estimated total sales reach $110 million? Use a graphing calculator to approximate the solution to the equation S(t) = 110.. (Round to two decimal places as needed.)
5. The remaining amount, A (in grams), of a substance undergoing ra- dioactive decay is given by the function A = f(t,C), where C is the initial amount of the substance present (in grams) and t is the time that has passed, in years. Use the contour plot of f shown to the right to answer the following questions. 40 15 20 10 30 20 (a) How much of the substance must be present in the initial sample in order for there to be 15 grams remaining after 2 years? Include 10 units. 1 2 3 4 6 (b) Sketch a graph of the cross-section of f in which t = 2. Carefully label your axes, and then briefly explain what this graph tells you. (c) Sketch a graph of the cross-section of f in which C = 40. Carefully label your axes, and then briefly explain what this graph tells you.
Answer No. 3 only. Thank you.

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