Final answer:
To find a formula for an exponential function passing through two points, we can use the general form of an exponential function and substitute the coordinates of the points into the equation. In this case, the formula for the exponential function is y = (8/25) * (5^x).
Step-by-step explanation:
To find a formula for an exponential function passing through the points (-3, 2/125) and (3, 250), we can use the general form of an exponential function, which is y = a × b^x, where 'a' is the initial value, 'b' is the base, and 'x' is the exponent.
Using the first point (-3, 2/125), we can substitute the values into the equation to get 2/125 = a × b^(-3). Simplifying this equation gives us a = 2/125 × b^(3).
Using the second point (3, 250), we can substitute the values into the equation to get 250 = a × b^3. Substituting the value of 'a' from the first equation gives us 250 = (2/125 × b^(3)) × b^3.
Simplifying this equation gives us b = 5.
Substituting the value of 'b' into the first equation gives us a = 2/125 × 5^3, which simplifies to a = 8/25.
Therefore, the formula for the exponential function passing through the points (-3, 2/125) and (3, 250) is y = (8/25) × (5^x).