Write an exponential function in the form \( y=a b^{x} \) that goes through the points \( (0,18) \) and \( (2,1458) \).

To find the exponential function in the form \( y=a b^{x} \) given the points \( (0,18) \) and \( (2,1458) \), we can start by substituting the first point into the equation. When \( x=0 \), \( y=18 \): \[ y = a b^{0} \implies 18 = a \cdot 1 \implies a = 18 \] Now we have \( y = 18 b^{x} \). Next, we use the second point \( (2, 1458) \): \[ 1458 = 18 b^{2} \] Dividing both sides by 18 gives: \[ b^{2} = \frac{1458}{18} = 81 \] Taking the square root of both sides, we get \( b = 9 \) (assuming we want the positive base). Hence, the function is: \[ y = 18 \cdot 9^{x} \] If you want to express it in a different exponential base, this can also be written in terms of \( e \) using properties of exponents, linking it beautifully to natural logarithms!