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Find a formula for \( f(x) \), an exponential function such that \( f(-5) = 170 \) and \( f(10) = 459 \).

**NOTE:** Round all numbers in the answer to four decimal places.

\[ f(x) = \] _______

Answer :

Final answer:

To find the formula for f(x), substitute the given values into the general form of an exponential function and solve for the constants a and b. The formula for f(x) is f(x) = 170 * (459/170)^x.

Explanation:

To find the formula for the exponential function f(x), we can use the given information. We know that f(-5) = 170 and f(10) = 459. We can set up two equations using the general form for an exponential function, f(x) = a * b^x. Substitute the values of x and f(x) into the equations and solve for a and b to find the formula for f(x).

Using the equation f(-5) = a * b^(-5), we can substitute f(-5) = 170 and solve for a. Similarly, using the equation f(10) = a * b^10 and substituting f(10) = 459, we can solve for b. Once we have a and b, we can write the formula for f(x) as f(x) = a * b^x.

Rounding all numbers to four decimal places, f(x) = 170 * (459/170)^x is the formula for the exponential function f(x).

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