Question

an exponential function of form f(x)=b^x includes the points (2, 16), (3, 64), and (4, 256) what is the value of b

Answer 1

The value of b is 4

Step-by-step explanation:

The form of an exponential function is $f(x)=a(b)^{x}$ , where

• a is the initial value (value f(x) at x = 0
• b is the growth/decay factor
• T find the values of a and b substitute x and f(x) by the coordinates of any points belong to the function

∵ $f(x)=b^{x}$

∵ The function includes the points (2 , 16) , (3 , 64) , (4 , 256)

- To find b substitute x and f(x) by the coordinates if any point above

∵ x = 2 and f(x) = 16

∴ $16=(b)^{2}$

- Take √ for both sides

∴ ± 4 = b

Substitute x by 3 and f(x) 64 to check your answer

∵ $64=(b)^{3}$

- Take ∛ for both sides

∴ 4 = b

∴ The value of b is 4 only

The value of b is 4

Learn more:

You can learn more about the inverse of the exponential function in brainly.com/question/11921476

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