Rates of Change Linear and Exponential

• Exponential Functions NEVER exceed Linear Functions

• Exponential Functions ALWAYS exceed Linear Functions

• The linear function exceeds the exponential function over the interval [0, 6]

• The exponential function exceeds the Linear functions over the interval [5, 6]

How would you describe the rate of change of these functions?

• Both functions have constant rate of change because they are exponential.

• Both functions have a variable rate of change because they are both exponential.

• A has a constant rate of change because it is linear and B has a variable rate of change because it's exponential

• A has a constant rate of change because it is quadratic and B has a variable rate of change because it's exponential

Which kitten grows fastest? What is it's rate of change?

• Kitten A with a rate of change of 3

• Kitten B with a rate of change of 4

• Kitten A with a rate of change of 4

• Kitten B with a rate of change of 3

Account R starts with $4, and triples each week. Account S starts with $800, and grows by $300 each week.

Which account shows a common factor?

• Account R

• Account S

Which statement below describes the comparison of rate of change between the linear function f(x) and the exponential function g(x).

• g(x) rate of change is ALWAYS greater than f(x) rate of change.

• g(x) is NEVER greater than f(x) rate of change.

• g(x) will eventually exceed the rate of change of f(x).

• There is not enough information to compare the rate of change of f(x) to g(x).

The number of grams, y, of a radioactive element that remains after t hours can be modeled by the equation y=2.45(0.84)^t. What is the rate of increase or decrease of this radioactive element?

• 16% increase per hour

• 84% increase per hour

• 84% decrease per hour

• 16% decrease per hour

What is the rate of change in the following function: g\left(x\right)=7-14x

• -14

• 7

• 14

• -14x

Compare the two linear functions listed below and determine which has a greater slope.

• Function 1 because the slope is 3/2

• Function 2 because the slope is 1

• Function 1 because the slope is 2/3

• They are equal 

The cost of Nate’s service is described by y = 4x + 6. The table shows the cost of Beth’s service. Which service is cheaper for 8 movies in one month?

• Beth's service ($38 vs. $40) is cheaper

• Nate’s service ($42 vs. $44) is cheaper

• Nate’s service ($38 vs. $40) is cheaper

• Beth's service ($42 vs. $44) is cheaper

For each input/output pair below, determine whether it satisfies Function f, Function g, Both functions, or Neither function. Choose one option for each blank section. Input: 1 Output: 6

• Function f

• Function g

• Both functions

• Neither function