Question

Find the formula for an exponential function that passes through the two points given.

(x, y) = (0,5) and (x, y) = (3, 40)

Answer 1

Answer: y = 5(2)^x.

Explanation:

Let's assume that the exponential function is of the form y = ab^x, where a and b are constants to be determined.

Using the point (0, 5):

5 = ab^0

5 = a

Using the point (3, 40):

40 = ab^3

Substitute a = 5 into the second equation:

40 = 5b^3

8 = b^3

b = 2

Therefore, the formula for the exponential function is y = 5(2)^x.