Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Without graphing, determine whether the function
y

=

(
5
.
2
)
x
represents exponential growth or exponential decay. Explain why.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years.

A coordinate graph is shown. The horizontal axis extends from 0 to 12 years. The vertical axis extends from 0 to 9500 with an axis label of 'Value' in dollars. A curve is graphed which begins at 0 comma 3500, then decreases passing through approximately 1 comma 2700

Write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Write the equation in logarithmic form.

125
4
3
=
625

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Evaluate the logarithm.

log
7
49
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Solve
ln

2

+

ln

x

=

5
. Round to the nearest thousandth, if necessary.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

The sales of lawn mowers t years after a particular model is introduced is given by the function
y

=

5500

ln
(
9
t

+

4
)
, where y is the number of mowers sold. How many mowers will be sold 5 years after a model is introduced? Round the answer to the nearest whole number.

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

In a particular region of a national park, there are currently 330 deer, and the population is increasing at an annual rate of 11%.

a. Write an exponential function to model the deer population in terms of the number of years from now.
b. Explain what each value in the model represents.
c. Predict the number of deer that will be in the region after five years. Show your work.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

In the equation
y

=

a
b
(
x
−
h
)
+
k
how does the value of k affect the graph?