Which of the following exponential functions goes through the points (1, 20) and (2, 80)?

To determine which exponential function passes through the points (1, 20) and (2, 80), we can represent an exponential function in the form of y = ab^x, where a is the initial value and b is the growth factor.

From the first point (1, 20), we substitute into the equation:

20 = ab¹ → 20 = ab (1)

Next, using the second point (2, 80):

80 = ab² → 80 = ab² (2)

Now we have two equations:

• Equation (1): 20 = ab
• Equation (2): 80 = ab²

We can solve for b by dividing equation (2) by equation (1):

80 / 20 = (ab²) / (ab) → 4 = b

Now that we have b = 4, we can substitute it back into equation (1) to find a:

20 = a(4) → a = 5

Therefore, the exponential function we are looking for is:

y = 5(4)^x

To verify, we can check both points:

• At x = 1: y = 5(4)¹ = 20
• At x = 2: y = 5(4)² = 80

Since both points satisfy the function, we have confirmed that the exponential function which goes through the points (1, 20) and (2, 80) is y = 5(4)^x.