Answer :

The value of f(0), to the nearest hundredth, is approximately 946.15.

We can use the general form of an exponential function, which is:

[tex]f(x) = a * b^x[/tex]

where a and b are constants.

To find the value of f(x), we need to determine the values of a and b. We can use the two given points (-3, 27) and (0.5, 83) to form two equations:

[tex]27 = a * b^(-3)[/tex]

[tex]83 = a * b^(0.5)[/tex]

We can solve for a in the first equation:

[tex]a = 27 / b^(-3)[/tex]

Substituting this value of a into the second equation:

[tex]83 = (27 / b^(-3)) * b^(0.5)[/tex]

Simplifying, we get:

[tex]83 = 27 * b^(3/2)[/tex]

[tex]b^(3/2) = 83 / 27[/tex]

[tex]b = (83 / 27)^(2/3)[/tex]

Now that we have found b, we can substitute it back into the first equation to solve for a:

[tex]27 = a * (83 / 27)^(-3/2)[/tex]

[tex]a = 27 * (83 / 27)^(3/2)[/tex]

Using the general form of an exponential function, we can find f(0) by setting x = 0:

[tex]f(0) = a * b^0[/tex]

f(0) = a

Substituting the values of a and b that we found earlier:

[tex]f(0) = 27 * (83 / 27)^(3/2)[/tex]

f(0) ≈ 946.15

Therefore, the value of f(0), to the nearest hundredth, is approximately 946.15.

To learn more about nearest hundredth please click on below link.

https://brainly.com/question/29083575

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