Academy Algebra II

1
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 gt 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
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)
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.
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
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.
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).
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.