1. 4-1:Exponential Growth and Decay
English Casbarro
Unit 4

2. Exponential Functions
If an output doubles every year, it can be modeled by an exponential function
The parent function is: f(x) = bx, where b is a constant and x is the independent variable.
b > 0, and b ≠ 1

3. Remember the graph on the introduction: y = 2x
Notice that as x decreases, the graph gets closer and closer to the x-axis.
The graph, however, will never touch the x-axis, so it is an asymptote.

4. b is the constant of growth if b > 1
The standard form of an exponential growth (decay) function:
a is the initial amount
b is the constant of growth if b > 1
b is the constant of decay if 0< b < 1
x is usually the time

5. For exponential growth, as the value of x increases,
the value of y increases. For exponential decay, as the value
of x increases, the value of y decreases, approaching zero.

7. You can model growth or decay by a
constant percent increase or decrease with
the following formula:
Number of time periods
Final amount
Initial amount
Rate of growth or decay
In the formula, the base of the exponential
expression 1 + r, is called the growth factor.
Similarly, 1 – r is called the decay factor.

11. 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.

12. Transformation of the graph

13. Turn in the following problems
The compound interest formula is , where A is the amount earned,
P is the principal, r is the annual interest rate, t is the time in years, and n is
the number of compounding periods per year. Harry invested $5000 at 5%
interest compounded quarterly(4 times per year).
a. How much will the investment be worth after 5 years?
b. When will the investment be worth more than $10,000?
c. What if Harry could have invested the same amount in an account that paid
5% interest compounded monthly (12 times per year). How much more would
his investment have been worth after 5 years?
2. What are the values of a and b in f(x) = abx in the graph
shown at the right?
3. The population of Midland, Texas was 89, 443 in 1990
and has increased at a rate of 0.6% per year since then.
Which function represents the Midland’s growth function
after t years?
89,443(1.6)t B. 89,443(1.06)t
C. 89,443(1.006)t D. 89,443(1.0006)t