8. The manager of an appliance manufacturing firm determines that when toasters are priced at p dollars apiece, the numbersold each month can be modeled by300A(p) =PThe manager estimates that t months from now, the unit price of the toasters will be p(t) = 0.04ť² + 18.5 dollars. At whatrate will the monthly demand for toasters, A(p), be changing two years from now? Will it be increasing or decreasing at thistime?

Answered: Image /qna-images/answer/45c7fe47-0199-436e-a408-e44cb20257e0.jpg

Answered: 8. The manager of an appliance…

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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Suppose that the production Q (in gallons of paint) of a paint manufacturer can be modeled by Q = 140K/2L/2, where K is the company's capital expenditures in thousands of dollars and L is the size of the labor force (in hours worked). Find aQ/ƏK when capital expenditures are $230,000 and the labor hours are 900. (Round your answer to two decimal places.) aQ/ək = Interpret aQ/ƏK. If labor hours remain at 900 and K increases by $1000, will increase about gallons of paint. Find aQ/ƏL when capital expenditures are $230,000 and the labor hours are 900. (Round your answer to two decimal places.) aQ/Ək = Interpret aQ/aL. If capital expenditures remain at $230,000 and L increases by one hour, Q will increase about gallons of paint. Need Help? Read It Watch It
The estimated value of a diamond purchased for investment purposes is determined by S(t) = 250(1.75)i . If the rate of depreciation is 7 percent under continuous compounding, how much should the diamond be held to maximize its current price?
1. The purchasing power P (in dollars) of an annual amount of A dollars after t years of 5% inflation decays according to the following formula P=Ae^-0.05t A. How long will it be before a pension of $80,000 per year has a purchasing power of $20,000? (Round your answer to the nearest dollar). B. How much pension A would be needed so that the purchasing power P is $40,000 after 11 years? (Round to the nearest dollar). 2. Suppose the supply of x units of a certain product at price P dollars per unit is given by P= 17 + 5ln(2x+1) How many units of the product would be supplied when the price is $47 each (round your answer to the nearest whole number).
3. Once an antibiotic is introduced to bacteria, the number of bacteria decreases exponentially. For example, beginning with 1 million bacteria, the amount present t days from the time streptomycin is introduced is given by the function A(t) = 1,000,000(2)-t/10. Rounding to the nearest thousand, determine how many bacteria are present after 1 week.
2. Consider a firm producing a single commodity. The total cost C(q) of producing q units of the commodity can be described by the equation C = q/2, where q denotes the number of units produced. The revenue function is given by r = 30- ln(2q + 1). Determine the output for maximum profit.
3. A principal of (A) OR is deposited in an account that pays A/100 interest compounded yearly. Account balance function in response of time (years)is B(y) = 1(1+ c)" I: initial value A=347, W=19, R=9347 c: interest compounded yearly v: time in vear a. Find the account balance after W months. b. Show by graphing if B(y) function is increasing or decreasing. c. After how many years the account balance will be (R) OR.
A company estimates that the cost of new capacity additions follows the function f(y) = 0.0358y0.66, where y is the number of units and f(y) in millions of dollars. Demand is increasing at a rate of 3,500 units per year. The company uses a 10% per year interest rate. What is the present value of the cost of the next nine capacity additions?
2. a. Write an exponential equation of the form y = a(b)* that passes through the points (1, 6.4) and (4, 3.2768). Explain how you got your answer OR show your work. b. Identify the percent change that is modeled by your equation in part a. In other words, identify whether your equation represents a percent increase or decrease AND how much is that percent increase or decrease.
3. During a period of 9 months, the number of people owning a flip-o-phone has increased from 285 000 to 315 000. Calculate how many months after the start of the 9-month-period we can expect 400 000 own- ers of a flip-o-phone if we assume that their number a. grows according to a linear function; b. grows exponentially; c. grows according to a formula of the form F(t) = 500 000 a ebt, where a and b are constants and where F denotes the number of owners of a flip-o-phone and t the time in months since the start of the 9-month-period.

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