Exponential Function - Rate of Change

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

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.

Answer explanation

To find the average rate of change from day 0 to day 5, use the formula \( \frac{f(5) - f(0)}{5 - 0} = \frac{1283 - 2000}{5 - 0} = -143.4 \). Thus, the correct choice is \( \frac{1283-2000}{5 - 0}=-143.4 \).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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 5 to day 15.

Answer explanation

To find the average rate of change from day 5 to day 15, use the formula \( \frac{f(15) - f(5)}{15 - 5} = \frac{528 - 1283}{10} = -75.5 \). Thus, the correct choice is \( \frac{528-1283}{15 - 5} = -75.5 \).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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

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Tags

CCSS.HSF-IF.C.7E

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

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. 

• 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

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