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
