Exponential
February 21, 2005
Exponential Review
Fill in the following table.
Exponential
Initial Value
Function
t
Growth or
Decay?
Growth or
Decay Factor
Growth or
Decay Rate
A = 4(1.03)
A = 10(0.98) t
1000
1.005
30
0.96
$50,000
Growth
7.05%
200 grams
Decay
49%
Applied Problem 1
The United States imported $495 billion worth of goods from abroad in 1990 and
$912 billion worth of goods in 1998.
a) Find a linear function of time since 1990.
b) Describe the slope in context of the problem.
c) Find an exponential function of time since 1990.
d) Describe the growth rate in context of the problem.
e) In 2003, the United State imported $1172 billion worth of goods. Which
model best fits? Explain.
Exponential
February 21, 2005
Applied Problem 2 – On your own.
In 1990, the United States produced $43 billion dollars of electronics and
electronic components. In 1994, the United States produced $58.2 billion dollars.
a) Find a linear function of time since 1990.
b) Describe the slope in context of the problem.
c) Find an exponential function of time since 1990.
d) Describe the growth rate in context of the problem.
e) In 1998, the United State produced $76 billion. Which model best fits?
Explain.
Exponential
February 21, 2005
Applied problem 3
In 1798 an economist named Malthus argued that population size can be
predicted from one year to the next by multiplying by a fixed amount. He also
argued that food production can be predicted from one year to the next by adding
a fixed quantity. The table below lists the world population in millions and food
production in millions of “food units”. A food unit is the amount of food necessary
to feed on person.
Year
World Population
(millions)
980
1254.4
1605.6
1800
1850
1900
Food Production (millions
of food units)
1200
1550
1900
a) Find the equation for the world population as a function of time.
b) Find the equation for the food production as a function of time.
c) According to the function that you found in part b), when will food
production reach 6060 million food units?
d) Based upon your equations, when will the world not have enough
food?
Homework
p. 269 #19, 20, 21, 25, 27