Academy Algebra II
7.7: Write and Apply Exponential
and Power Functions
Write an Exponential Function y = abx
That Passes Through Two Points.

Write the exponential function passing
through (1, 12) and (3, 108).
1.) Substitute the coordinates into: y = abx
12 = ab1
108 = ab3
Write an Exponential Function y = abx
That Passes Through Two Points.

Write the exponential function passing
through (1, 12) and (3, 108).
2.) Solve for a in the first equation: 12 = ab1
and substitute into the second equation: 108 = ab3
12
12  3

a
108  
b
b
 b 
108  12b 2
9  b2
3b
b > 0 in exponential
functions.
Write an Exponential Function y = abx
That Passes Through Two Points.

Write the exponential function passing
through (1, 12) and (3, 108).
3.) Plug in b-value and solve for a.
12
a
b
x
y

4

3
12
a
3
a4
Write an exponential function
y = abx whose graph passes
through the given points.
1.) (1, 3), (2, 12)
Write an exponential function
y = abx whose graph passes
through the given points.
2.) (3, 8), (6, 64)
b
Write a Power Function y = ax
That Passes Through Two Points.

Write the power function passing through
(3, 2) and (6, 9).
Substitute the coordinates into: y = axb
and solve (just like the exponential function).
Hint: Use logs.
Write a power function y = axb whose
graph passes through the given points.

(2, 1), (7, 6)
Write a power function y = axb whose
graph passes through the given points.

(3, 4), (6, 15)
Use Exponential Regression

Find an exponential model for the data. Use the model
to predict the number of scooters sold in the 8th year.
Year, x
1
# of scooters sold, y 12
89: Graphing Calculator: Select
data/matrix editor.
Create new or open.
Input data (to clear data, press
F1 (tools), select 8: clear editor.
Turn on plots: Press F2 (plot
setup), press F1 (define), fill in
c1 and c2 for x and y.
2
3
4
5
6
7
16 25 36 50 67 96
83/84: Graphing Calculator:
Press Stat, select edit.
Input x in list1 and y in list2.
Zoom – select zoomstat to
view graph
(make sure plot 1 is on:
press y = and highlight plot1)
Use Exponential Regression

Find an exponential model for the data. Use the model
to predict the number of scooters sold in the 8th year.
Year, x
1
# of scooters sold, y 12
89: Graphing Calculator: To
view graph, adjust window
and press graph. To
calculator regression, press
F5 (calc), change calculation
type to ExpReg, type c1 and
c2 for x and y, and store
regression to y1(x).
2
3
4
5
6
7
16 25 36 50 67 96
83/84: Graphing Calculator:
Press Stat, arrow over to
Calc, Arrow down to ExpReg.
To view exponential function
on graph: Input equation in
y1. Press graph.
Use Power Regression

Find a power model for the data. Use the
model to predict the weight of a bird with
wingspan of 4.5 feet.
Wingspan (ft), x 1.9
2.92 3.41 5.35 8.4
Weight (lbs), y
1.04 1.69 6.76 16.03
.23
Input data in just like the previous question.
When selecting regression, select: PwrReg.