Find the formula for an exponential function that passes through the two points given. (x, y) = (0, 6) and (x, y) = (3, 48)

Question

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

(x, y) = (0, 6)

 and (x, y) = (3, 48)

Answer 1

The formula for a general exponential function can be written as: y = ab^x

Let's plug in the first point, (0,6), into our general exponential function to solve for a. b⁰ = 1, so it's a good way to not deal with b for now.

y = ab^x

6 = ab^x*0= ab⁰ = A(1) = A

Therefore, A = 6.

Now, let's plug in the second point, (3,48), into our general exponential function with A plugged in as well. This will give us b.

y = 6b^x

48 = 6b³

8 = b³

8^1/3 = b

b = 2

Let's plug a and b into the general exponential function:

y = 6(2^x)