Final answer:
The general form of an exponential function is f(x) = ab^x, and by solving the equations based on the given points, the exponential function is derived as f(x) = 36∙0.5^x. However, none of the provided options matches this derived function.
Step-by-step explanation:
To find an exponential function f(x) that passes through the points (1, 18) and (2, 9), we can use the general form of an exponential function, which is f(x) = abx. For the given points, we can set up two equations based on the function's values at x=1 and x=2:
- f(1) = ab1 = 18
- f(2) = ab2 = 9
From the second equation, we observe that ab2 = a(b2) = 9, and since ab = 18 from the first equation, we get b2 = 18 / ab. Therefore, b2 = 9 / 18 = 1/2, giving us b = √(1/2) = 0.5. Substituting back into the first equation, a = 18 / b = 18 / 0.5 = 36, yielding the equation f(x) = 36 ∙ 0.5x.
However, none of the given options matches this equation. Option B, f(x) = 18 ∙ 0.5x is closest, but the initial value a does not match the determined value of 36. Thus, the given options do not include a correct exponential function that passes through the points (1, 18) and (2, 9).