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If [tex]f(x)[/tex] is an exponential function where [tex]f(2) = 9[/tex] and [tex]f(2.5) = 94[/tex], find the value of [tex]f(4)[/tex], to the nearest hundredth.

Answer :

Final answer:

To find the value of f(4) in an exponential function given f(2) = 9 and f(2.5) = 94, calculate the growth factor and apply it to f(2) to find f(4) as approximately 1110.77.

Explanation:

Exponential function f(x) can be analyzed using the given data. First, we need to determine the growth factor of the exponential function, which is the ratio of f(2.5) to f(2). Then, we can use this growth factor to find the value of f(4) by applying it to f(2) = 9.

Calculate the growth factor: 94/9 = 10.44

Use the growth factor to find f(4): f(4) = f(2) * growth factor¹.⁵ = 9 * 10.44¹.⁵ = approximately 1110.77

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