5. The exponential function \( f(x) \) passes through the points \( (0,150) \) and \( (1,90) \). (3) Find a formula. Show work. Your formula should begin with " \( y= \) ".

To find the formula for the exponential function \( f(x) = ab^x \) that passes through the points \( (0, 150) \) and \( (1, 90) \), we can use these points to set up equations. 1. From the point \( (0, 150) \), we substitute into the equation: \[ f(0) = ab^0 = a = 150. \] 2. Substituting the point \( (1, 90) \): \[ f(1) = ab^1 = 150b = 90. \] To find \( b \), we solve for \( b \): \[ b = \frac{90}{150} = \frac{3}{5}. \] So, we have \( a = 150 \) and \( b = \frac{3}{5} \). Finally, the formula is: \[ y = 150 \left( \frac{3}{5} \right)^x. \]