Write an exponential function in the form \( y=a b^{x} \) that goes through the points \( (0,20) \) and \( (3,2500) \).

To find the exponential function \( y = a b^x \) that passes through the points \( (0,20) \) and \( (3,2500) \), we can start by identifying \( a \) and \( b \). 1. From the point \( (0,20) \), we can say: \[ y = a b^0 = a = 20 \] So, we have \( a = 20 \). 2. Next, use the point \( (3,2500) \): \[ 2500 = 20 b^3 \] Dividing both sides by 20, we get: \[ b^3 = \frac{2500}{20} = 125 \] Taking the cube root of both sides: \[ b = 5 \] Now, substituting \( a \) and \( b \) back into the original function gives us: \[ y = 20 \cdot 5^x \] So the exponential function is: \[ y = 20 \cdot 5^x \]