Exponential Rate of Change

What type of pattern do exponential functions have?

• Adds by the same number every time

• Multiplies by the same number every time

• Square roots all the inputs

• Squares all the inputs

Is the graph linear, exponential, or neither?

• Linear

• Exponential

• Neither

Pick the equation that is exponential growth

• y=2(0.5)^x

• y = 0.5(2)^x

Pick the equation that is exponential decay

• y=2000(0.88)

• y=0.5(1.88)

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).

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).

• A/F
• B/G
• C/H
• D/J

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

Find the average rate of change over the given interval. 

• 4

• 7

• 7/3

• 3/7

The number of decks of popular trading cards is a function f of the number of days d since the shipment arrived. Calculate the average rate of change from day 0 to day 5.