Writing Exponentials Wrap Up Section 5.8
Algebra II
Name: ________________________
Date: _____________ Period: _____
PLEASE SHOW ALL WORK ON A SEPARATE PIECE OF PAPER
1.) A 1990 Lexus was purchased and depreciates 8% every year. In 1993 the Lexus costs $39,375.
(a) How would you find the price of the car in the year 1994?
(b) Find the price of the car when it was purchased in 1990.
(c) Suppose the depreciation is exponential. Find a formula for the value of the car at time t where t
represents the number of years after 1990.
(d) Suppose instead the depreciation is linear. Assume the starting value of the car you determined in (b)
as well as the given price of the car in 1993. Find a formula for the value of the car as a function of the
years since you purchased the car in 1990.
(e.) If this were your car and you were trading it after 4 years, which depreciation model would you
prefer (exponential or linear)?
2.) Find an exponential equation for the curve below. (NOTE: Be mindful of the scale on the x axis)
3.) You decide to buy another Lexus in 1999 and miraculously the cost is the same, $39,375. You own
the car until 2006 when you decide to sell. According to Kelly Blue book the car has depreciated 46%
during its first seven years.
(a) What is the value of the car in 2006?
(b) Suppose the depreciation is exponential. Find a formula for the value of the car at time t.
4.) The population of Florida has increased, on average, at a rate of 8% per year since 1953. In 1993,
the population of Florida was 13 million.
(HINT: The answer is 598,402 people…but how?)
A.
What was the population in 1953?
B.
Write an equation that models the population, P, as a function of t, years since 1953.
C.
What was the population in 1969?
D.
When was the population 5 million?
5.) The black bear population of Florida has decreased, on average, at a rate of 6% per year since 1953.
In 1953, the black bear population was 11,000.
A.
Write an equation that models the black bear population, B, as a function of t, years since 1953.
B.
Find the black bear population in 1993.
6.) The New York Times reports that wildlife biologists have found a direct link between the increase in
human population and the decline of local black bear population in Florida. When the human
population reaches 32 million, what will be the black bear population?
7.) Provide a sketch of the following functions and provide the domain and range of each without a
calculator.
A.
f(x) = 3(1.2)x
B.
g(x) = 10(1.1)x
C.
h(x) = – 5 (½)x
D.
Will f(x) = g(x)? How do you know?
8.) Determine if each table can be modeled by an exponential function. If so model using both a closed
and recursive rule.
x
f(x)
x
g(x)
x
h(x)
0
200
5
3
1
12
1
100
6
3.6
3
108
2
50
7
4.32
5
972
3
25
8
5.184
7
8748
4
12½
9
6.2208
9
78,732