Algebra II Trig
Notes on Exponential Growth and Decay 4.11/5/15
I. Exponential Functions
A. Given the table, what patterns do you notice?
- As the x increases, the y values double
- The y values will never equal zero
B. Growth that doubles can be modeled using a function with a variable as an exponent. This is called an
exponential function.
C. The parent exponential function is where the base b is a constant and the exponent is the
independent variable. b > 0 and b 1.
D. Write a function to represent the table:
E. Graph the function. What do you notice?
- There is a horizontal asymptote at y = 0
- Crosses the y-axis at (0, 1): will this always happen?
II. Exponential Growth and Decay
A. A function of the form , with a > 0 and b > 1, is an exponential growth function. The values of
y increase as the values of x increase.
B. A function of the form , with a > 0 and 0 < b < 1, is an exponential decay function. The values
of y decrease and the values of x increase.
C. Tell if the function represents exponential growth or decay and then graph:
i. ii.
III. Modeling Exponential Growth and Decay
A. You can model growth or decay by a constant increase or decrease with the following formula:
- is the final amount
- a is the initial amount
- r is the rate
- t is the number of time periods (typically in years)
B. The base of is called the growth factor.
C. The base of is called the decay factor.
D. The value of a truck bought new for $28,000 decreases 9.5% each year. Write an exponential function
and graph the function. Use the graph to predict when the value will fall to $5000.
t = 17.3 years
E. Adam purchased a rare 1959 Gibson Les Paul guitar in 2000 for $12,000. Experts estimate that its value
will increase by 14% per year. Find when the value of the guitar will reach $60,000.
t = 12.29 years (after 2012)