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    Exponents, graphs, and equations

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    1. A factory working at 83% of capacity produces 231 widgets per day. How many widgets would it produce if it worked at full capacity?

    2. Solve for X: x - 2.4 = 1.5

    3. Simplify: (Recall: x-3 = 1/x3)

    91/2 a2/3 b-1/5

    4. PROTRAC, Inc. produces two lines of heavy equipment. One of these product line (E-9), termed earthmoving equipment, is essentially for construction applications. The other line (F-9) is for forestry use. The two lines are produced in the same departments (A and B) with the same machines. For next month's production, Dept. A has 150 hours available and Dept. B has 120 hours available. The table below summarizes this information:

    Per E-9 10 12
    Per F-9 15 8

    Total Available 150 120

    Let X represent the number of E-9's produced next month and let Y represent the number of F-9's produced next month. Write and expression involving X and Y based on the data above for Dept. A.

    5. Under which scenario is the final price of the stock higher? Explaiin
    A. The price goes up by 5% and then down by 5%
    B. The price goes down by 5% and then up by 5%

    6. Sketch the graph of the line y= -2x + 4. What is the slope of the line?

    7. Find the point where the two lines meet.

    y = -2x + 4
    x - 2y = 4

    8. For the function f(x) = x - 2
    x - 4

    A. Find f(8)
    B. Are there any values for which f(x) is not defined? Explain.

    9. A company has the following total cost and total revenue functions when producing and selling Q units of a product.

    TC = 15Q + 100 TR = Q2

    Find the breakeven values. Also, sketch below the cost and revenue functions showing the breakeven values. Put Q on the horizontal Axis and TC and TR on the vertical axis.

    10. Hoe much money will you have in an account two years from now, if today you deposit $100 into that account and the interest rate is 10% per year compounded semi-annually?

    11. What amount would be needed now in order to generate $1000 five years from now id the interest is 3.7% per year compounded annually?

    12. Solve for X: logx 16 = 4

    Evaluate to 3 decimal places LN 7 =

    13. An economist want to use the percentage change in productivity in the U.S. (X) to predict the percent change in the Standard & Poor's index (Y). He ran a regression using data for a period of 50 years and the following model was produced:
    Y = -5.0 +7X

    A. Use the model to predict the percentage change in the S&P if the percentage change in productivity is @% (X=2)
    B. Identify the Y-intercept of this line. Interpret that number in terms of the model.
    C. Identify the slope. Interpret that number in terms of the model.

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    Solution Summary

    There are a variety of topics covered in this solution including: percentage, solving for a variable, simplifying exponents and fractions, graphing equations of lines, points of intersection, points at which a function is undefined, logarithms and natural logs.