FROM THE GIVEN INPUT AND OUTPUT FIND THE EXPONENTIAL FUNCTION

Every exponential function will be in the form y = abx

  • If b > 1, then it must be exponential growth function.
  • If 0 < b < 1, then it must be exponential decay function.

Find an exponential function having the given values.

Problem 1 :

f(0) = 3 and f(1) = 15

Solution :

Exponential function will be in the form

y = abx

From the given inputs and outputs, we can understand that the points (0, 3) and (1, 15) on the exponential function.

Applying (0, 3)

3 = ab0

3 = a(1)

a = 3

Applying (1, 15)

15 = ab1

15 = (3)b

b = 15/3

b = 5

Applying the values of a and b, we get the required exponential function

y = 3(5)x

Problem 2 :

f(0) = 5 and f(3) = 40

Solution :

Exponential function will be in the form

y = abx

From the given inputs and outputs, we can understand that the points (0, 5) and (3, 40) on the exponential function.

Applying (0, 5)

5 = ab0

5 = a(1)

a = 5

Applying (3, 40)

40 = ab3

40 = (5)b3

b= 40/5

b3 = 8

b = 2

Applying the values of a and b, we get the required exponential function

y = 5(2)x

Problem 3 :

f(0) = 64 and f(2) = 4

Solution :

Exponential function will be in the form

y = abx

From the given inputs and outputs, we can understand that the points (0, 64) and (2, 4) on the exponential function.

Applying (0, 64)

64 = ab0

64 = a(1)

a = 64

Applying (2, 4)

4 = ab2

4 = 64b2

b= 4/64

b2 = 1/16

b = 1/4

Applying the values of a and b, we get the required exponential function

y = 64(1/4)x

Problem 4 :

f(0) = 80 and f(4) = 5

Solution :

Exponential function will be in the form

y = abx

From the given inputs and outputs, we can understand that the points (0, 80) and (4, 5) on the exponential function.

Applying (0, 80)

80 = ab0

80 = a(1)

a = 80

Applying (4, 5)

5 = 80b4

5/80 = b4

 b= 1/16

b = 1/2

Applying the values of a and b, we get the required exponential function

y = 80(1/2)x

Problem 5 :

f(2) = 10 and f(4) = 40

Solution :

Exponential function will be in the form

y = abx

From the given inputs and outputs, we can understand that the points (2, 10) and (4, 40) on the exponential function.

Applying (2, 10)

10 = ab2

Applying (4, 40)

40 = ab b2

40 = 10 b2

4 = b2

b = 2

Applying the value of b2, we get

10 = 4a

a = 10/4

a = 5/2

Applying the values of a and b, we get

y = (5/2)(2)x

Recent Articles

  1. Graphing Exponential Growth and Decay Worksheet

    Dec 08, 23 08:03 AM

    graphing-exponential-growth-and-decay-s1
    Graphing Exponential Growth and Decay Worksheet

    Read More

  2. Finding the Specific Term from the Given Explicit Formula Worksheet

    Dec 08, 23 07:32 AM

    Finding the Specific Term from the Given Explicit Formula Worksheet

    Read More

  3. Finding Roots of Complex Numbers Using De Moivres Theorem Worksheet

    Dec 08, 23 07:10 AM

    Finding Roots of Complex Numbers Using De Moivres Theorem Worksheet

    Read More