1. 7.7: Write and Apply Exponential and Power Functions
Academy Algebra II
7.7: Write and Apply Exponential and Power Functions

2. 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

3. 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
b > 0 in exponential
functions.

4. 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.

5. Write an exponential function y = abx whose graph passes through the given points.
1.) (1, 3), (2, 12)

6. Write an exponential function y = abx whose graph passes through the given points.
2.) (3, 8), (6, 64)

7. Write a Power Function y = axb 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.

8. Write a power function y = axb whose graph passes through the given points.
(2, 1), (7, 6)

9. Write a power function y = axb whose graph passes through the given points.
(3, 4), (6, 15)

10. 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 2 3 4 5 6 7
# of scooters sold, y 12 16 25 36 50 67 96
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.
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)

11. 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 2 3 4 5 6 7
# of scooters sold, y 12 16 25 36 50 67 96
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).
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.

12. 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
.23
1.04
1.69
6.76
16.03
Input data in just like the previous question.
When selecting regression, select: PwrReg.