Answer :
Final answer:
To find the value of f(6.5), we can use the given information and the properties of exponential functions. First, solve the equations for f(-4) and f(4) to find the values of a and b. Then, substitute x = 6.5 into the exponential function to find the value of f(x).
Explanation:
To find the value of f(6.5), we can use the given information and the properties of exponential functions. Since we know f(-4) = 1 and f(4) = 69, we can find the base of the exponential function. Let's denote the base as b. Using the formula for exponential growth, we can write the equation:
f(x) = a * b^x
Plugging in the values for f(-4) and f(4), we get:
1 = a * b^(-4)
69 = a * b^4
We can solve these two equations simultaneously to find the values of a and b. Once we have the values, we can substitute x = 6.5 into the function f(x) to find its value.
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