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
#SPJ4
