Respuesta :

Ashraf82

The value of b is 4

Step-by-step explanation:

The form of an exponential function is [tex]f(x)=a(b)^{x}[/tex] , 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

∵ [tex]f(x)=b^{x}[/tex]

∵ 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

∴ [tex]16=(b)^{2}[/tex]

- Take √ for both sides

∴ ± 4 = b

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

∵ [tex]64=(b)^{3}[/tex]

- 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

#LearnwithBrainly

MrRoyal

The value of b in the exponential function is 4

The points on the function are given as:

(2, 16), (3, 64), and (4, 256)

The value of b is then calculated as:

[tex]b = \frac{y_2}{y_1}[/tex]

So, we have:

[tex]b = \frac{64}{16}[/tex]

Evaluate the quotient

[tex]b = 4[/tex]

Hence, the value of b is 4

Read more about exponential functions at:

https://brainly.com/question/11464095

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