Do Not Use a Calculator on This Part of the Exam

MAC 2233Name______

Test 2Spring 2005Absences______

DO NOT USE A CALCULATOR ON THIS PART OF THE EXAM.

______1. Write in exponential form: -4 = log3

______2. Write in logarithmic form: e5.55 = 258

______3. Compute the average rate of change over the interval [10.00,25.00] specifying the units of measurement.

p($) / 10.00 / 15.00 / 25.00
q(p) (items) / 150 / 250 / 300

______4. For the function whose graph is shown below, find the average rate of change of profits over the period from 1992 to 1996. Use correct units.

5. For each of the given slopes, determine at which of the labeled points on the graph the tangent line has that slope.

______a.0

______b.-1

______c.1

______d.3

______6.Estimate the derivative of at x = 6 from the following table of average rates.

/ 1 / 0.1 / 0.01 / 0.001 / 0.0001
Ave. rate of change of over / 37 / 34.3 / 34.03 / 34.003 / 34.0003
/ -1 / -0.1 / -0.01 / -0.001 / -0.0001
Ave. rate of change of over / 31 / 33.7 / 33.97 / 33.997 / 33.9995

______7. If function is differentiable at , then is (you will have more than one

answer):

a.The average value of the function over the interval .

b.The instantaneous rate of change of at .

c.The slope of the tangent line at the point on the graph where x = 7.

Use the shortcut rules to evaluate the following derivatives:

______8. Find f’(x) if f(x) = 5x4 – 3x + 2

______9. Find if y = 3x-4 – 2x-1

______10. Find f’(x) if f(x) =

11. The Old World Furniture Company’s yearly profits are modeled by P(t), where P(t) is in thousands of dollars, and t represents the number of years since 2000. The company’s profits for the year 2000 were $256 thousand and were increasing at a rate of $12 thousand per year. During the period 2000 to 2004, the company’s average profits were $290 thousand per year. Use this information to fill in the blanks below.

______a. P’(0) = ?

______b. The average rate of change of P over [0,4] is ?

______c. P(0) = ?

MAC 2233 Test 2Name______

YOU MAY USE A CALCULATOR ON THIS PART OF THE EXAM. IF NECESSARY, ROUND FINAL ANSWERS TO HUNDREDTHS UNLESS OTHERWISE INDICATED. YOU ARE ENCOURAGED TO USE THE 2ND TRACE, FUNCTION ON YOUR CALCULATOR WHEN APPROPRIATE FOR THE WORD PROBLEMS.

______1. Find if f(x) if f(x) = -4x2.5 +

______2. Determine if p(t) = 2t3 – 3t2

______3. Give the average rate of change of f(x) = 3x2 – 5x over the interval [2, 5].

Round answer to nearest hundredth.

______4. Given the function f(x) = 1 – 2x3 , find the slope of the tangent line to the graph

of the function of f(x) at x = -1.

______5. Write the equation of the tangent line to the function f(x) at x = -1 in problem 4.

Note that you found the slope of this tangent line in problem 4.

6. The graph shows the approximate annual sales of in-ground swimming pools. Also shown is the tangent line (and its slope) at the point corresponding to year 2000.

______6a. How many pools were sold in 2000?

______6b. How fast are swimming pool

sales changing in 2000?

______

______7. How long will it take a $10,000 investment to be worth $100,000 is it is invested at 10% compounded quarterly? (Set decimal places in MODE to 4 places to work the problem, but round your final answer to hundredths.)

______8. How long will it take an investment to double if it is invested at 6% compounded continuously? (Set decimal places in MODE to 4 places to work the problem, but round your final answer to hundredths.)

For problems 9 and 10: A farmer has created a function, which he believes will predict the price of

corn over the next six months. The function is

where represents selling price per bushel in dollars, and t is time in months since January 1, 2000. (Thus t = 1 represents February 1, 2000).

9. Determine the average rate of change of over the period January 1 through May 1, and interpret your results. Round answer to nearest hundredth.

______

10. Determine how fast the price is changing on January 1, 2000. (Round to nearest hundredth)

______

11. The number of Roman Catholic nuns P(t), in thousands, can be modeled by the equation

P(t) = -0.15t2 +0.50t + 130, where t is the years since December 1995 and P(t) is in thousands.

Find the instantaneous rate of change of P(t) in December 1997 and interpret your answer. Round answer to nearest whole number.

______

______12. A particle moves along a straight path where the distance s, in feet traveled in time t seconds is given by

s(t) = t2 + 3t – 1

Find the velocity of the particle at t = 4 seconds. Give units in your answer.

______13. I took the iLrn quiz and made at least 75 on it. Write yes or no.