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AA3-1 Investigation -- exponential growth and decay cloned 1/19/2021

Last updated about 4 years ago
19 questions
1

Describe what is happening to f(x) as x increases:

1

Write an equation for f(x)

1

Describe what is happening to f(x) as x increases:

1

Write an equation for f(x)

1

Describe what is happening to f(x) as x increases:

1

Write the equation of f(x), if possible

1

Describe what is happening to f(x) as x increases:

1

Write the equation of f(x), if possible.

You were likely unable to write the equation for the last two tables. They are exponential functions. In AA3-3, we will study graphing exponential functions in the form:
However, for now, we will write exponential functions centered at the origin so (h,k) is (0,0). As a result, we will write exponential functions in the form:
-- a is the starting value (f(0))
-- b is the rate of growth or decay (what we are multiplying by each time)
-- x is the number of times something occurs. It is often, but not always, an amount of time.
1

Because f(x) increases as x increases, this function is a model of exponential growth.
Write the exponential equation for this table:

1

Because f(x) decreases as x increases, this function is a model of exponential decay.
Write the exponential equation for this table:

1

Complete the table for f(x)=4(3)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

1

Is f(x) = 4(3)x a model for exponential growth or decay?

1

Complete the table for f(x)=4(0.75)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

1

Is f(x) = 4(0.75)x a model for exponential growth or decay?

1

Predict whether f(x) = 1/2 (5)x is a model for exponential growth or decay?

1

Complete the table for f(x)= 1/2 (5)x by evaluating f(0), f(1), f(2), and f(3).
Don't forget (anything)0 = 1.
Depending on the calculator, you use the ^ button or ab or xy to create an exponent.

1

Is f(x) = 1/2 (5)x is a model for exponential growth or decay?

1

How do you know if an exponential function will model growth or decay?

1

Match each exponential function:

Draggable itemCorresponding Item
decay
f(x)=8(1.7)x
neither
f(x)=8(0.7)x
growth
f(x)=8(1/4)x
neither
f(x)=1/4(8)x
growth
f(x)=8(0)x
growth
f(x)=8(1)x
decay
f(x)=1(8)x