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 " \( y= \) ". (1) Use your formula to find \( f(2) \). Do not round. (

Given that the exponential function \( f(x) \) passes through the points (0,150) and (1,90), we can use these points to find the formula of the exponential function. Let's denote the exponential function as \( f(x) = a \cdot b^x \), where \( a \) and \( b \) are constants. Since the function passes through the point (0,150), we have: \[ f(0) = a \cdot b^0 = a = 150 \] Since the function passes through the point (1,90), we have: \[ f(1) = a \cdot b^1 = 90 \] Substituting the value of \( a \) from the first equation into the second equation, we get: \[ 150 \cdot b = 90 \] \[ b = \frac{90}{150} = \frac{3}{5} \] Therefore, the formula of the exponential function is: \[ f(x) = 150 \cdot \left(\frac{3}{5}\right)^x \] Now, we can use this formula to find \( f(2) \): \[ f(2) = 150 \cdot \left(\frac{3}{5}\right)^2 \] Let's calculate this value. Calculate the value by following steps: - step0: Calculate: \(150\left(\frac{3}{5}\right)^{2}\) - step1: Evaluate the power: \(150\times \frac{9}{25}\) - step2: Multiply: \(54\) The value of \( f(2) \) is 54.