Question

If f(x) is an exponentilal function where f(-4)=17 and f(4)=34, then find the value of f(-2.5), to the nearest hundredth.

Answer 1

To find the value of f(-2.5), we can use the given values of f(-4) and f(4) to determine the base of the exponential function. Then, we can substitute -2.5 for x to find the value of f(-2.5).

Step-by-step explanation:

To find the value of f(-2.5), we need to determine the exponential function that relates the given inputs and outputs. We can start by finding the base of the exponential function using the given values of f(-4) and f(4).

Since f(-4)=17 and f(4)=34, we can write the general form of the exponential function as
`f(x) = a * b^x`, where a is the initial value (f(-4)=17) and
`b^8=34/17.`

Next, we can substitute -2.5 for x in the equation
`f(x) = a * b^x` to find the value of f(-2.5).