GRAPHING EXPONENTIAL FUNCTIONS

An exponential function is non linear function of the form 

y = abx, where a ≠ 0 and b ≠ 1 and b > 0

  • Where a > 0 and b > 1, then the function is an exponential growth function.
  • Where a > 0 and 0 < b < 1, then the function is an exponential decay function.

Tell whether the function represents exponential growth or exponential decay. Then graph the function.

Problem 1 :

f(x) = 2(1/3)x

Solution :

f(x) = 2(1/3)x

Write the form of  y = abx

Here, a = 2, b = 1/3

Since, the value of b is 0 < 1/3 < 1. The given function f(x) is a exponential decay function. Use a table to graph the function.

let f(x) = y

put x = -1

y = 2(1/3)x

y = 2(1/3)-1

y = 6

put x = 0

y = 2(1/3)0

y = 2

put x = 1

y = 2(1/3)1

y = 2/3

put x = 2

y = 2(1/3)2

y = 2(1/9)

y = 2/9

Some of the points are (-1, 6) (0, 2) (1, 2/3) and (2, 2/9).

graphingexfunctionq1.png

Problem 2 :

f(x) = 4(3)x

Solution :

Given function, f(x) = 4(3)x

Comparing with y = abx

Here, a = 4, b = 3

Since, the value of b is > 1. The given function f(x) is a exponential growth function. Use a table to graph the function.

put x = -2

f(x) = 4(3)x

y = 4(3)-2

y = 4(1/3)2

y = 4(1/9)

y = 4/9

put x = -1

y = 4(3)-1

y = 4(1/3)1

y = 4(1/3)

y = 4/3

put x = 0

y = 4(3)0

y = 4

put x = 1

y = 4(3)1

y = 12

So, the points are (-2, 4/9) (-1, 4/3) (0, 4) and (1, 12).

graphingexfunctionq2

Problem 3 :

f(x) = (1/4)x

Solution :

Given function, f(x) = (1/4)x

Comparing the function with y = abx

Here, a = 1, b = 1/4

Since, the value of b is 0 < b < 1. The given function f(x) is a exponential decay function. Use a table to graph the function.

let f(x) = y

put x = -2

f(x) = (1/4)x

y = (1/4)-2

y = (4)2

y = 16

put x = -1

y = (1/4)-1

y = 4

put x = 0

y = (1/4)0

y = 1

put x = 1

y = (1/4)1

y = 1/4

put x = 2

y = (1/4)2

y = 1/16

Some of the points are (-2, 16) (-1, 4) (0, 1) (1, 1/4) and (2, 1/16).

graphingexfunctionq3.png

Problem 4 :

f(x) = (4/3)x

Solution :

Given function, f(x) = (4/3)x

Comparing with y = abx

Here, a = 1, b = 4/3

Since, the value of b is >1. The given function f(x) is a exponential growth function. Use a table to graph the function.

let f(x) = y

put x = -2

f(x) = (4/3)-2

y = (3/4)2

y = 9/16

put x = -1

y = (4/3)-1

= (3/4)1

y = 3/4

put x = 0

y = (4/3)0

y = 1

put x = 1

y = (4/3)1

y = 4/3

put x = 2

y = (4/3)2

y = 16/9

Some of the points are (-2, 9/16) (-1, 3/4) (0, 1) (1, 4/3) and (2 16/9).

graphingexfunctionq4.png

Problem 5 :

f(x) = 0.5(4)x

Solution :

Given function, f(x) = 0.5(4)x

Write the form of y = abx

Here, a = 0.5, b = 4

Since, the value of b is >1. The given function f(x) is a exponential growth function. Use a table to graph the function.

put x = -1

f(x) = 0.5(4)x

y = 0.5(4)-1

= 0.5(1/4)

= (1/2)(1/4)

y = 1/8

put x = 0

y = 0.5(4)0

= 0.5

y = 1/2

put x = 1

y = 0.5(4)1

= 0.5(4)

= 1/2(4)

y = 2

put x = 2

y = 0.5(4)2

= 0.5(16)

= 1/2(16)

y = 8

Some of the points are (-1, 1/8) (0, 1/2) (1, 2) and (2, 8).

graphingexfunctionq6.png

Problem 6 :

f(x) = 3(0.75)x

Solution :

Given function, f(x) = 3(0.75)x

Write the form of y = abx

Here, a = 3, b = 0.75

Since, the value of b is 0 < b < 1. The given function f(x) is a exponential decay function. Use a table to graph the function.

put x = -2

f(x) = 3(0.75)-2

y = 3(0.75)-2

= 3(3/4)-2

= 3(4/3)2

= 3(16/9)

= 48/9

y = 16/3

put x = -1

y = 3(0.75)-1

= 3(3/4)-1

= 3(4/3)1

= 12/3

y = 4

put x = 0

y = 3(0.75)0

= 3(3/4)0

= 3(4/3)0

= 3(1)

y = 3

put x = 1

y = 3(0.75)1

= 3(3/4)1

y = 9/4

graphingexfunctionq6n

Problem 7 :

f(x) = 2(0.8)x

Solution :

Given function, f(x) = 2(0.8)x

Write the form of y = abx

Here, a = 2, b = 0.8

Since, the value of b is 0 < b < 1. The given function f(x) is a exponential decay function. Use a table to graph the function.

put x = -2

f(x) = 2(0.8)-2

y = 2(0.8)-2

y = 2(4/5)-2

= 2(5/4)2

= 2(25/16)

= 50/16

y = 25/8

put x = -1

y = 2(0.8)-1

y = 2(4/5)-1

= 2(5/4)1

= 10/4

y = 5/2

put x = 0

y = 2(0.8)0

y = 2

put x = 1

y = 2(0.8)1

= 2(4/5)

y = 8/5

So, the points are (-2, 25/8) (-1, 5/2) (0, 2) and (1, 8/5).

graphingexfunctionq7

Problem 8 :

f(x) = 5(2)x

Solution :

Given function, f(x) = 5(2)x

Write the form of y = abx

Here, a = 5, b = 2

Since, the value of b is > 1. The given function f(x) is a exponential growth function. Use a table to graph the function.

put x = -3

f(x) = 5(2)x

y = 5(2)-3

= 5(1/2)3

y = 5/8

put x = -2

y = 5(2)-2

= 5(1/2)2

= 5(1/4)

y = 5/4

put x = -1

y = 5(2)-1

= 5(1/2)1

= 5(1/2)

y = 5/2

put x = 0

y = 5(2)0

= 5(1)

y = 5

put x = 1

y = 5(2)1

y = 10

graphingexfunctionq8.png

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