MATH 121 001 Calculus I for Natural Science, Social Science, and Business

Test 1 9:05-9:55 Stright 226

Dr. H. Edward Donley

February 13, 2015 Name

A=P1+rnnt

1. (9 points) A human with a 15-inch-long femur (leg bone) is 60 inches tall and a human with a 20-in-long femur is 70 inches tall. Find a linear equation for the height of a person as a function of the femur length.

2. (9 points) The age (x) and systolic blood pressure (y, in mm of mercury) of 33 U.S. women, aged 22 to 81, were used to construct the least squares line y = 1.22x + 81.54.

a) What are the units for the slope and what does it represent?

b) What does the correlation coefficient, r = 0.74, say about the relationship between x and y?

c) Use this line to predict the systolic blood pressure for a 50 year old U.S. woman.

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3. (7 points) A candy shop's fixed costs for producing chocolate are $20. Variable costs are $2 per pound. Write an equation for the total cost of producing x pounds of chocolate. What is the cost of producing 8 pounds of chocolate?

4. (8 points) Find the interest earned on $4000 invested at 6% annual interest, compounded monthly for 10 years?

5. (9 points) If $1000 is investment at 4% annual interest compounded continuously, use logarithms to find when the investment will reach $1500.


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6. (11 points) Algebraically find

7. (10 points) Find

8. (8 points) Given the graph at the right, what is the value of:

a) f(1)

b)

c)

d)

9. (8 points) Give all values of x where fx=x2-9x-3 is discontinuous and find the value of the limit of the function at those values of x.

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10. (7 points) A GPS station west of the San Andreas Fault on the Pacific Plate is moving slowly northwest. In 2007, researchers recorded the station 33 mm northwest of its original position. In 2012, they recorded it 195 mm northwest of its original position. On average, how fast was the station (and thus the Pacific Plate) moving between 2007 and 2012?

11. (12 points) Use the limit definition of the derivative to find the derivative of
f(x) = x2 – 5x + 2.