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Quantitative Reasoning Questions

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1. Evaluate the function f(x) = 9x - 6 for x=0 and x=5.

2. Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85, where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

3. Find the slope of the line through the points ( 5, -5) and ( 6, -1)

4. Kafka Inc. imports hard drives and sells them on the internet. The profit is given by the equation P = 140n - 8500, where n is the number of hard drives sold. Graph P = 140n - 8500 for n < 1000. Estimate the profit, to the nearest ten dollars, corresponding to the sale of 875 hard drives.

5. When $ 8600 is invested in a savings account paying simple interest for the year, the interest, i in dollars, can be obtained from the equation i = 8600r , where r is the rate of interest in decimal form. Graph i = 8600r , for r up to and including a rate of 15%. If the rate is 12%, how much interest is earned?

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Solution Summary

There are five problems. Solutions to given problems depicts the steps to determine the value of function at given point, slope of a line passing through two given points and cost minimizing number of repairs. It also depicts the methodology to find the value of given functions at a desired point.

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Please refer attached file for missing graphs.

1. Evaluate the function f(x) = 9x - 6 for x=0 and x=5.
f(x)=9x-6
f(0)=9*0-6=3
f(5)=9*5-6=39

2. Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

C(x)=4x^2-296x+85
Differentiate with respect to x, we get
C'(x)=8x-296
Put C'(x)=0
8x-296=0
x=296/8=37
Let us find second derivative of C(x)
C''(x)=8
We find ...

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  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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