Final answer:
To write the exponential function from given points, find the y-intercept as the starting value and solve for the base using the second point. The function is f(x) = -2·3x.
Step-by-step explanation:
To write the exponential function represented by the points (2, −18) and (0, −2), we can assume the function has the form f(x) = abx. Given the point (0, −2), we can find a because f(0) = ab0 = a·1, so a = −2. Substituting this into the function with the second point (2, −18), we get:
−18 = −2b2
Dividing both sides by −2 gives us b2 = 9, so b = 3 or b = −3. However, since we are dealing with an exponential function, which requires a positive base, we choose b = 3. Therefore, our function is f(x) = -2·3x.