Question

If f(x) is an exponential function where f(4) = 7 and f(5.5) = 53, then find thevalue of f(5), to the nearest hundredth.

Answer 1

To find the value of f(5), we can create two equations using the given points and solve for the constants in the exponential function.

Step-by-step explanation:

To find the value of f(5), we need to determine the exponential function represented by f(x). We know that f(4) = 7 and f(5.5) = 53. We can use these two points to create two equations and solve for the unknown values in the exponential function. Let's assume the exponential function is in the form f(x) = a * b^x, where a and b are constants.

Substituting the known values, we get:

1. f(4) = 7 = a * b^4
2. f(5.5) = 53 = a * b^5.5

We can then solve these equations simultaneously to find the values of a and b. Once we have a and b, we can substitute x = 5 into the function f(x) to find the value of f(5), to the nearest hundredth.