Final answer:
To find the value of f(9.5), use the given information to find the constants a and b in the exponential function f(x) = a * b^x. Set up equations using the given x and f(x) values, solve them simultaneously to find a and b, and then plug in x = 9.5 to find f(9.5).
Step-by-step explanation:
In order to find the value of f(9.5), we can use the information given in the problem. We know that f(x) is an exponential function, so we can express it as f(x) = a * b^x, where a and b are constants. We are given that f(1.5) = 6 and f(5.5) = 26f. To find the values of a and b, we can use these two equations. Plug in the values for x and f(x) in the equations and solve for a and b.
Using the given values, we can set up the following equations:
6 = a * b^1.5
26f = a * b^5.5
Solve these equations simultaneously to find the values of a and b.
Once you have the values of a and b, you can plug in x = 9.5 into the function and solve for f(9.5).