Final answer:
To find the value of f(6) in the exponential function f(x), we need to solve for the base and exponent using the given values of f(2) and f(3). The equation for the exponential function is approximately f(x) ≈ 6.3947 * (58/23)^x. Plugging in x = 6, we find that f(6) is approximately 1016.73.
Step-by-step explanation:
To find the value of f(6), we need to determine the equation for the exponential function f(x).
Given that f(2) = 23 and f(3) = 58, we can set up a system of equations to solve for the base and the exponent.
f(2) = a*b² = 23
f(3) = a*b³ = 58
Dividing the second equation by the first equation, we get:
b³/b² = 58/23
b = 58/23
Substituting the value of b in either equation, we can solve for a:
a = 23/(58/23)²
a ≈ 6.3947
Therefore, the equation for the exponential function is f(x) ≈ 6.3947 * (58/23)ˣ
Now, we can find the value of f(6) by plugging in x = 6 into the equation:
f(6) ≈ 6.3947 * (58/23)⁶ ≈ 1016.73