Exercise Set 6
Table 13: Population,
P
(
t
), of Las Vegas
t
years after 1980
t
0
10
20
30
P
(
t
)
164,674
259,834
484,487
583,756
1. Refer to the population of Las Vegas, NV, for given years as shown in Table 13.
(a) Using the population of Las Vegas in 1980 and 2010, build an exponential model for
P
(
t
).
(b) Use your exponential model to predict the population of Las Vegas in 1990. How does
your prediction compare with the actual population at that time?
(c) Use your exponential model to predict in what year the population of Las Vegas will be
600,000.
(d) Using the population of Las Vegas in 1980 and 2010, build a linear model for
P
(
t
).
(e) Do you think the linear model or the exponential model is a better fit to the data?
Explain.
2. When buying a new car, one consideration is how fast the car loses value, known as the
depreciation rate. For example, one version of the Jeep Liberty loses value more rapidly than
some of its competitors. From the initial purchase price of $23,395, an owner can expect the
value of the car 5 years later to be $15,239.
(a) What is the average dollar value decline per year during the first 5 years of ownership?
(b) Use an exponential model produce a function that gives the value of the Jeep in terms
of the number of years,
t
, since the Jeep was new.
(c) Use your model to predict the value of the Jeep when it was 3 years old.
(d) When will the value of the Jeep decline to $5,000?
3. A baseball is launched into the air from a height of 2 meters and with an initial upward
velocity of 25 meters/second. The ball’s height above ground is given by the equation
H
(
t
) =

4
.
9
t
2
+
vt
+
h
, where
H
is in meters and
t
is in seconds.
(a) Write an equation to model the height of a ball.
(b) How long is the ball in the air?
(c) What is the maximum height reached by the ball?
4. Oscar charges $5 per linear foot to paint any standard outdoor wooden fence, plus $20 to
cover incidental items, such as brushes.
(a) Write a function equation that gives the cost to paint a fence of length
L
feet.
22
(b) What is the cost to paint a fence 50 feet long?
(c) If Oscar recently painted a fence and charged $110, how long was the fence?
5. Titanium44 is a radioactive isotope with a halflife of 63 years.
(a) Write an exponential equation to model the amount,
A
(
t
), remaining after
t
years from
an initial sample of 20 mg.
(b) How much of the sample will remain after 30 years?
(c) When will the sample decay to 2 mg?
Combining Functions
Often in mathematics, we are interested in using existing functions to create new functions. In this
section and the next, we will look at some common ways of building new functions.
Goals:
•
F: Be able to determine a composition of functions given in any form (graph, table, equation).
•
F: Be able to perform arithmetic (sum, difference, product, quotient) on functions given in
any form (graph, table, equation).
Example 47.
You have already seen that function notation uses parentheses to mean something
other than multiplication. When examining functions, the function use of parentheses will be the
norm. For instance, if
f
(
x
) = 2
x
and
g
(
x
) = 3
x
2

2
x

5
, then we can define
h
(
x
) =
f
(
x
) +
g
(
x
)
.