Final answer:
To write the function formula for f, we use the exponential form of an exponential function and the given points (0, 19) and (1, 17). By setting up a system of equations and solving for the variables, we can find the values of a and b in the function formula. The final function formula for f is f(x) = 19 * (17/19)^x.
Step-by-step explanation:
Given that f is an exponential function and we know two points on the function, we can write the function formula for f using the exponential form: f(x) = a * b^x, where a is the initial value and b is the base. We are given that f(0) = 19 and f(1) = 17. Plugging these values into the formula, we can set up two equations:
19 = a * b^0, which simplifies to 19 = a
17 = a * b^1, which simplifies to 17 = a * b
Since we know that a = 19, we can substitute this value into the second equation:
17 = 19 * b
Solving for b, we get: b = 17/19
Therefore, the function formula for f is: f(x) = 19 * (17/19)^x