Exponential Function 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

Answer explanation

Exponential functions increase by multiplying the previous value by a constant factor. This means they multiply by the same number every time, distinguishing them from linear functions that add a constant.

Tags

CCSS.HSF-IF.C.8B

What is the Average rate of change formula? (Rate of change of Exponential Functions)

• (f(a) + f(b)) / (b + a)

• (f(b) - f(a)) * (b + a)

• (f(a) * f(b)) / (b - a)

• (f(b) - f(a)) / (b - a)

Answer explanation

The average rate of change of a function between two points a and b is calculated using the formula (f(b) - f(a)) / (b - a). This measures how much the function value changes per unit change in x, making it the correct choice.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Find the average rate of change over the given interval. 

• 4

• 7

• 7/3

• 3/7

Answer explanation

To find the average rate of change, use the formula (f(b) - f(a)) / (b - a). After calculating for the given interval, the result simplifies to 7/3, making it the correct choice.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Find the average rate of change over the given interval. 

• -2

• 2

• -1

• -0.5

Answer explanation

The average rate of change is calculated as (f(b) - f(a)) / (b - a). Given the values, this results in -2, confirming that the correct answer is -2.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

• A/F
• B/G
• C/H
• D/J

Tags

CCSS.HSF-IF.C.8B

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

Tags

CCSS.HSF-IF.C.8B

In Jack and the beanstalk, the beanstalk grows very rapidly. It began at a length of 3 ft and grew at a rate of 14% per minute Write the exponential function for this example

• y=6(0.14)^x

• y=3(17)^x

• y=3(1.14)^x

• y=3(0.86)^x

• y=6(1.04)^x

Tags

CCSS.HSF.LE.A.2

What is the equation of the graph shown, and what is the y-intercept?

• y = 1⁄3 (3)^x ; a = 1⁄3

• y = 1⁄3 (3)^x ; a = 3

• y = 3 (1/3)^x ; a = 1⁄3

• y = 3 (1/3)^x ; a = 3

Tags

CCSS.HSF.LE.A.2

Find the average rate of change over the given interval.

• 3

• 1.5

• 1

• 0.67

Answer explanation

The average rate of change is calculated as (f(b) - f(a)) / (b - a). If the values at the endpoints of the interval yield a difference of 3 over a span of 2, the average rate of change is 1.5, making it the correct choice.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

What type of function is f(x)=2(3^x) ?

• Quadratic

• Linear

• Exponential