D2 Unit 8 Algebra 1 Notes
Exponential Functions
Name: ____________________
Date: ____________ Per: ____
An equation where the independent variable appears in the exponent is called an exponential equation.
We can recognize that an equation is exponential in three ways.
An equation is exponential if the independent variable appears in the exponent.
Exponential:
𝑦 = 2(4)𝑥
𝑦 − 3𝑥 = −2
Non-exponential: 𝑦 = 𝑥 2 − 4
𝑥 3 + 𝑦 3 = 16
5𝑦 = −4 ∙ 2𝑥
2
𝑦=𝑥
9𝑥 − 15𝑦 = 7
𝑥𝑦 = 3
𝑦 = 2𝑥 − 3
A graph is exponential if the points form a curve that starts out slow, and then becomes quickly steep.
The rate of change will vary by a common ratio for every point of increase.
Exponentials:
Non-exponential:
An exponential function will always have the same ratio between y values. When the change in x is
constant, the y values will have a common ratio. (Multiply by the same number)
Exponential:
x
y
x
y
0
3
-8
6
1
12
-6
3
2
48
-4
1.5
3
192
-2
0.75
4
768
0
0.375
NonExponential:
x
y
1 2 3 4 5
1 2 5 10 17
Write the equation of the exponential function below. Exponential functions have the
General form 𝒇(𝒙) = 𝒂(𝒃)𝒙 , where a is the starting amount (y-intercept) and b is the common ratio.
𝒓
𝒏
Growth 𝒚 = 𝒂(𝟏 + 𝒓)𝒕 , Decay 𝒚 = 𝒂(𝟏 − 𝒓)𝒕 , Compound interest 𝑨 = 𝑷(𝟏 + )𝒏𝒕 , and half life 𝑨 =
𝑷(𝟎. 𝟓)𝒕 .
1.
2.
3.
4. Ronnie bought a home for $165,000 whose value is increasing at a rate of 2.5% per year.
5. Jenni opens a certificate of deposit worth $2000 in 2016. The interest rate is compounded quarterly
at 1.5%.
6. Strontium-25 has a half life 3 minutes long. How much Strontium-25 is left from a 200 gram sample
after 30 minutes?
7. Which of the following data sets is best described by an exponential model?
a.
{(1, 3), (2, 6), (3, 9), (4, 12)}
b. {(1, 3), (2, 6), (3, 12), (4, 24)}
c.
{(1, 3), (2, 5), (3, 9), (4, 15)}
d. {(1, 3), (2, 6), (3, 15), (4, 24)}
8. Which is the equation of the graph of f(x)?
9. Write the equation of the exponential
function that passes through the two
points (0, 6) and (1, 12).
Equation:_______________________________