Question

Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 19)(0,19) and (3, 9728)(3,9728).

Answer 1

Answer:

y = 19*(8)^x

Step-by-step explanation:

We want to write an equation like:

y = a*b^x

That goes through the points (0, 19) and (3, 9728)

Then, when x = 0, we must have y = 19

Replacing those values in the equation we get:

19 = a*b^0 = a*1 = a

19 = a

Then the equation is:

y = 19*b^x

We also know that when x = 3, y = 9728

If we replace these values in the equation, we get:

9728 = 19*(b)^3

Let's solve this for b.

9728/19 = b^3

512 = b^3

∛512 = b = 8

Then the equation is:

y = 19*(8)^x