Final answer:
To find the exponential function that contains the points (0,5) and (2,20), substitute the x and y values into the general form of an exponential function. The resulting equation is y = 5 * (2^x).
Step-by-step explanation:
To find the exponential function that contains the points (0,5) and (2,20), we can use the general form of an exponential function, which is y = a * (b^x). We need to find the values of a and b that satisfy both points.
Using the first point (0,5), we substitute x=0 and y=5 into the equation and get 5 = a * (b^0), which simplifies to 5 = a * 1, so a = 5.
Using the second point (2,20), we substitute x=2 and y=20 into the equation and get 20 = 5 * (b^2), which simplifies to 4 = b^2. Solving for b, we find b = 2.
Therefore, the exponential function that contains the points (0,5) and (2,20) is y = 5 * (2^x).