GRAPHING EXPONENTIAL FUNCTIONS

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 = ab^x

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

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

Problem 2 :

f(x) = 4(3)^x

Solution :

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

Comparing with y = ab^x

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.

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

Problem 3 :

f(x) = (1/4)^x

Solution :

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

Comparing the function with y = ab^x

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

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).

Problem 4 :

f(x) = (4/3)^x

Solution :

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

Comparing with y = ab^x

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

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).

Problem 5 :

f(x) = 0.5(4)^x

Solution :

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

Write the form of y = ab^x

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 = 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).

Problem 6 :

f(x) = 3(0.75)^x

Solution :

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

Write the form of y = ab^x

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.

Problem 7 :

f(x) = 2(0.8)^x

Solution :

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

Write the form of y = ab^x

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.

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

Problem 8 :

f(x) = 5(2)^x

Solution :

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

Write the form of y = ab^x

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.