Pre-Calc Quest Review

1) Solve the following expressions without a calculator:

a) log₂ x = 3 b) log₃ x = 2 c) log₃ (1/9) = x d) log_x 64 = 3/4

e) log _-4 x = 1/2 f) log₃ 1 = x g) log₇ 0 = x h) log_x (1/216) = 3/2

i) log_1/2 x = 7 j) log₃ 3⁵ = x k) log_x (1/8) = 3 l) log₃ (-9) = x

For the following problems, show calculations for each step.

2) Suppose that the number of bacteria per square millimeter in a culture in the bioloby lab is increasing exponentially with time. On Tuesday, there are 2000 bacterial/mil². On Thursday, the number increased to 4500.

a) Find the equation to model the problem.

b) Predict the number of bacteria/mil² in the culture next Tueday.

c) Using logs, predict when the number of bacteria reaches 10,000.

3) Before you were born, Uncle Fred gave you $1200.00. It is now worth $25,983.42. It was in a CD earning 6.34% compounded continuously, how long ago did Uncle Fred invest the money?

4) Oliver Sudden is driving along a straight, level highway at 64 km/h when his car runs out of gas. As he slows down, his speed decreases exponentially with the number of seconds since he ran out gas, dropping to 48 km/h after 10 seconds.

a) Find the equation to model the problem.

b) Predict Oliver’s speed after 25 seconds?

c) Using logs, find the time when Oliver’s speed will be 10 km/h? 2 km/h?

d) Why would this model fail for large values of time?

5) The rebound heights for a super ball are modeled by the equation y = 5.65(.862)^x .

Using logs and graphing, find the number of bounces that will occur when the ball’s rebound height is less than 5%.