Mathematics

An exponential function has the form $f(x) = a \cdot b^x$, where the initial value $a$ and base $b$ determine both the starting point and the direction of growth. Since your curve passes through $(0,18)$, you know immediately what $a$ must be. For the curve to decrease as $x$ increases, the base $b$ must be between 0 and 1—think of it as repeatedly multiplying by a fraction, which shrinks the output each step. Use these two constraints to identify which function fits.

An exponential function has the form $f(x) = a \cdot b^x$, where the initial value $a$ and base $b$ determine both the starting point and the direction of growth. Since your curve passes through $(0,18)$, you know immediately what $a$ must be. For the curve to decrease as $x$ increases, the base $b$ must be between 0 and 1—think of it as repeatedly multiplying by a fraction, which shrinks the output each step. Use these two constraints to identify which function fits.