Exam 4A - Math 135 - Applied Algebra and Trigonometry (WWW)
Name _________________________
Campus _______________________
Mrs. Donna Tupper

Answer all questions and show all work to be graded. Where applicable, NO credit will be given for answer only responses. Make sure the testing center gives you a copy of the formula sheet.

1. For f(x) = 5^x, determine f(5), f(0), f(3), f(-1) and f(-3). Then graph the function.

ANSWER:   f(5) = 5⁵ = 3125

                    f(0) = 5⁰ = 1

                    f(3) = 5³ = 125

                    f(-1) = 5^-1 = 0.2

                    f(-3) = 5^-3 = 0.008

2.  Suppose you invest $1500 in an account with an annual interest rate of 4.75%, compounded continuously. You do not make any withdrawals during this period, so the interest will itself earn interest. How much money will be in the account after 2 years?

A = Pe^rt = 1500e^(.0475*2) = $1649.49

3.  Strontium-90 decays at the rate of 3.05% per year. If a nuclear power plant has 250kg of Strontium-90, how much will be remaining in 50.0 year?

A = Pe^(-rt) = 250e^{(-.0305 * 50)} = 54 years

4.  Convert to exponential form (there are more than one of these on the test) log ₂ 512 = 9.

log ₂ 512 = 9  implies 512 = 2⁹

5.  Convert to logarithmic form (there are more than one of these too) 8² = 64.

8² = 64  implies log₈ 64 = 2

6.  For log _b 729= 6, find the value of b.

Converting to exponential form, you have log _b 729= 6  implies 729 = b⁶

Now 729 = 3⁶, so b must equal 3.  Note, you can factor 729 if you need to find out the power a number is raised to.

7.  Represent log 26.1 = 1.4166 in exponential form.

Raising both sides to the power e, you get 26.1 = e^1.4166

8.  Solve 3.5e^x = 10. Round X to 3 decimal places.

First, divide both sides by 3.5.  That gives you

e^x = 10 / 3.5.

Now take the natural log of both sides and you get x = ln ( 10 / 3.5) = 1.05.

9.  Contract the following logarithm. 3 log x + log y - 4 log z

(log x³ * log y ) / (log z⁴)

10.  Expand the following logarithm. log _b sqrt(xy/z²).   

logb (xy / z²) ^0.5

0.5 log_b (xy / z²)  =

0.5 [log_b x + log_b y - log_b z²]  =

0.5 [log_b x + log_b y - 2log_b z]  =

0.5 log_b x + 0.5 log_b y - log_b z

11.  Solve for x: 2^x = 256

256 = 2⁸, so x = 8

12.  Mrs. Tupper bought a hot caramel latte. Afterwards, she decided she wanted an iced caramel latte instead. The latte has a cooling rate of 2.1% per minute. If she places her hot latte, which is 100.0^oC in a freezer which is 0.0^oC for 90.0 minutes, what will be the new temperature of her latte?

T = 100e -^{(.0201 * 90)} = 15^o.  That is one really iced latte!

NOTE: The time in the formula is in minutes, that means the time in the question must also be in minutes.  If I give the time in hours, then convert it to minutes before you plug anything into the formula.