Exponential Functions

Average Rate of Change

100

What is another name for the average rate of change formula?

The slope formula

200

What is the average rate of change formula?

m = (y₂-y₁) / (x₂-x₁)

300

Find the average rate of change given the points (0, 1) and (3, 8).

m = 7/3

400

Given the graph of the function f(x) = .5^x - 2, state the average rate of change over the interval -3<x<-1.

m =-3

500

Given the equation y = 12475.93 (.87)^x , find the average rate of change over the interval 1 < x < 3 rounded to the nearest hundredth.

m=-1319.31

Exponential Regression

100

Once you update the spreadsheet for a linear regression on your calculator what do you press after menu?

4, 1, 3

200

Once you update the spreadsheet for an exponential regression and press menu what are your next 3 key strokes.

4, 1, A

300

Given the exponential equation y = 12475.93(.87)^x , determine the value of the car to the nearest cent after 8 years.

$4094.75

400

Find the equation of an exponential function in the form y=ab^x that passes through the point (0, 1928), (1, 2237), (2, 2802), (3, 3403), and (4, 3878), rounded to the nearest hundredth.

y = 1917.36(1.20)^x

500

Find an equation of an exponential function in the form y=ab^x that passes through the points (2, 12905) and (4, 9959).  Round to the nearest hundredth.

y = 16722.46 (.88)^x

Functions

100

Given f(x) = 3x + 4, find f(2).

f(2) = 10

200

Given: f(x) = 2x² + 4x -1, find f(-2).

f (-2) = -1

300

Given: f(x) = 3(6)^x +11, find f(0).

f(0) = 14

400

State whether the equation y = 1200(2)^x is growth or decay and why.

Growth

Why - Left to right, low to high 

or the base (2) is greater than 1.

500

State whether the equation y=4(.5)^x is growth or decay and why.

Decay

Why:  Left to right, high to low

or because the base (.5) is between 0 and 1

Rounding

100

Round 827.1234 to the nearest tenth.

827.1

200

Round 454.23587 to the nearest thousandth.

454.236

300

Round 92.49218 to the nearest hundredth.

92.49

400

Round 0.8342346 to the nearest cent.

0.83 or .83

500

Round 900.9974 to the nearest tenth

901.0

Transformations

100

Given the equation y = 2^x-5, what is the equation of the parent graph?

y = 2^x

200

Given the equation y = 4^{x + 1} + 7, find the equation of the asymptote.

y = 7

300

Given the equation y = (2)^x-1 +5, identify the transformation from the parent graph.

The graph moved right 1 and up 5.

400

If the equation y = (1.25)^x is translated two units to the right and 7 units down, write the equation of the new graph.

y = (1.25)^x-2 -7

500

If the equation y = (2.9)^x+4 , determine the end behavior. 

As x approaches - infinity, y approaches 0

As x approaches + infinity, y approaches + infinity