Find the equation of an exponential function (y=ab^x+k) that passes through the points (2,264) and (6,4044) and has a horizontal asymptote of y=12. Show all steps.

Answer 1

If the asymptote is 12, k = 12

y = ab^x + 12

We have (2, 264) and (6, 4044).

Thus,

264 = ab^2 + 12

4044 = ab^6 + 12

252 = ab^2

4032 = ab^6

Divide the second equation by the first

16 = b^4

b = 16^(1/4) = 2^4^(1/4) = 2^1 = 2

Then, ab^2 = 252

4a = 252

a = 63

y = 63 * 2^x + 12