Rates of Change Linear and Exponential

Calculate the average rate of change for the function over the given interval:
g\left(x\right)=3\cdot\left(\frac{1}{4}\right)^x -3\le x\le0

(a)  

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Linear or Exponential?

• Linear

• Exponential

Linear or Exponential?

• Linear

• Exponential

• The linear function grows faster than the exponential function.

• The exponential function grows faster than the linear function.

• Both functions grow at the same rate.

• The growth rates cannot be compared.

Which of the following functions has a constant rate of change?

Tags

CCSS.HSF-LE.A.1B

Why is this function linear?

• This is a linear function because it does not have a constant rate of change

• This is a linear function because it creates a curved line.

• This is a linear function because it have a constant rate of change.

• This is a linear function because it's y-intercept is (0,2)

Tags

CCSS.HSF-LE.A.1B

The rate of change of two functions are being compared. One function, f(x) is represented by the equation f(x) = 5x + 9, while the other function, g(x) is represented in the table. Which is true?

• The rate of change for

  f(x) is less than the

  rate of change for g(x).

• The rate of change for

  g(x) is less than the rate

  of change for f(x)

• The rate of change for

  f(x) and g(x) are equal.

• The rates of change

  cannot be compared

  because f(x) is a linear

  function and g(x) is an

  exponential function.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

The table represents some points on the graph of a linear function. What is the rate of change of y with respect to x for this function?

Tags

CCSS.HSF-LE.A.1B

The graph shows the volume of a gas sample as the temperature changes and the pressure remains constant. Which of the following best represents the rate of change in the volume of the gas sample with respect to the temperature?

Tags

CCSS.HSF.IF.B.4

The graph shows the height of a tree every year. Which of the following is true about the rate of change of the tree's growth?

• The tree grew about 1 foot per year.

• The tree grew about 2 feet per year.

• The tree grew about 4 feet per year.

• The tree grew about 20 feet per year.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6