Often sales of a new product grow rapidly at first and then level off with time. This is the case with the sales represented by the function S(t) = 100-100t¹, where trepresents time in years. Find the rate of change of sales for the following number of years.a. 4 yearsThe rate of change in sales after 4 years is(Type an integer or decimal rounded to the nearest thousandth as needed.)b. 8 yearsThe rate of change in sales after 8 years is(Type an integer or decimal rounded to the nearest thousandth as needed.)

Given function is: S(t)=100-100t^(-1), where t represents time in years.

Answered: Often sales of a new product grow…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Predict the percentage of female high school graduates in 2026. Round to the nearest tenth (1 decimal place). _______ Predict instantaneous rate of change of the percentage of female high school graduates in 2033. Round to the nearest hundredth (2 decimal places). _______ % per year
K The following table gives the monthly premiums for an insurance policy on people of various ages. a. Find an exponential function that models the monthly premium as a function of age. b. Find the quadratic function that is the best fit for the data. c. Graph each function with the data points to determine which model is the better fit. a. The exponential function that models the data is y= (Use integers or decimals rounded to the nearest thousandth as needed for any numbers in the expression.) Age 35 40 45 50 55 Monthly Premium (S) 120 151 219 334 532 Age 60 65 70 75 Full data set O Monthly Premium (S) 980 1789 3208 5729
. Investments If $5500 is invested for x years at 12%interest, compounded quarterly, the future value thatresults is S = 5500(1.03) 4xdollars.a. Graph this function for 0 <= x <= 8.b. Use the graph to estimate when the money in theaccount will double.
Element X is a radioactive isotope such that its mass decreases by 20% every year. Ifan experiment starts out with 730 grams of Element X, write a function to representthe mass of the sample after t years, where the monthly rate of change can be foundfrom a constant in the function. Round all coefficients in the function to four decimalplaces. Also, determine the percentage rate of change per month, to the nearesthundredth of a percent.
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Graph the function
2. You bought a new computer for $2,500. Four years later, your computer is valued at $1,250. a. Assume that the cost function will be linear and write a linear function to describe the cost of the computer ?t years after you bought it. b. Assume that the cost function will be exponential (think of exponential decay) and write an exponential function to describe the cost of the computer ?t years after you bought it. c. For each function you just wrote, find the rate at which the cost is depreciating 3 years after you bought it. d. Which function do you think would be more accurate? Write a complete sentence or two describing why you think so.
3. Caroline puts S400 into a savings account that earns 6% annually. Write a function that represents this situation, where t is the time in years. Solve algebraically after how many years she will get $1200 in her account (round it to the nearest year).
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