4. Suppose a company wants to introduce a new machine that will produce a rate of annual savings (in dollars) given by the function S'(x), where x is the number of years of operation of the machine, while producing a rate of annual costs (in dollars) given by the function C'(x) S'(x) = 212 – x², C'(x)=x² + x. a. For how many years will it be profitable to use this new machine? The number of profitable years is b. What are the net total savings during the first year of use of the machine? The net total savings during the first year of use of the machine is $ (Round to the nearest dollar as needed.) c. What are the net total savings over the entire period of use of the machine? The net total savings over the entire period of use of the machine is $ (Round to the nearest dollar as needed.)

4. Suppose a company wants to introduce a new machine that will produce a rate of annual savings (in dollars) given by the function S'(x), where x is the number of years of operation of the machine, while producing a rate of annual costs (in dollars) given by the function C'(x) S'(x) = 212 – x², C'(x)=x² + x. a. For how many years will it be profitable to use this new machine? The number of profitable years is b. What are the net total savings during the first year of use of the machine? The net total savings during the first year of use of the machine is $ (Round to the nearest dollar as needed.) c. What are the net total savings over the entire period of use of the machine? The net total savings over the entire period of use of the machine is $ (Round to the nearest dollar as needed.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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4. Suppose a company wants to introduce a new machine that will produce a rate of annual savings (in dollars) given by the
function S'(x), where x is the number of years of operation of the machine, while producing a rate of annual costs (in
dollars) given by the function C'(x)
6.
S'(x) = 212 - x², C'(x) =x² +x.
a. For how many years will it be profitable to use this new machine?
The number of profitable years is
b. What are the net total savings during the first year of use of the machine?
The net total savings during the first year of use of the machine is $
(Round to the nearest dollar as needed.)
c. What are the net total savings over the entire period of use of the machine?
The net total savings over the entire period of use of the machine is $
(Round to the nearest dollar as needed.)

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