Answered

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If f(x)f(x) is an exponential function where f(-1)=5f(−1)=5 and f(7)=32f(7)=32, then find the value of f(4)f(4), to the nearest hundredth

Sagot :

Using an exponential function, it is found that the value of the function when x = 4 is of f(4) = 15.95.

What is an exponential function?

It is modeled by:

[tex]y = ab^x[/tex]

In which:

  • a is the initial value.
  • b is the rate of change, as a decimal.

In this problem, we have that f(-1)=5, hence:

[tex]5 = ab^{-1}[/tex]

[tex]\frac{a}{b} = 5[/tex]

a = 5b

We also have that f(7)=32, hence:

[tex]32 = ab^7[/tex]

Since a = 5b:

[tex]5b^8 = 32[/tex]

[tex]b = \sqrt[8]{\frac{32}{5}}[/tex]

b = 1.2612.

a = 5b = 5 x 1.2612 = 6.306.

Hence the function is given by:

[tex]y = 6.306(1.2612)^x[/tex]

Then, when x = 4, we have that:

[tex]y = 6.306(1.2612)^4 = 15.95[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

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