Question

Write an exponential function y = abx for a graph that includes (1, 15) and (0, 6).

Answer 1

\[y=ab^x\] if \(x=0\) you ge t
\[6=ab^0=a\times 1=a\]telling you \(a=6\)

Answer 2

y = ab^x , so using the point (x,y) = (0,6) --> 6 = ab^0 ; b^0 = 1 so 6 = a(1) . Therefore, a = 6

Using the second point (1, 15) and the fact that a = 6 --> 15 = (6)b^1 or 15 = 6b
Therefore, 15/6 = b (or 5/2 = b, when you reduce the fraction)

Finally, substituting 6 for a and 5/2 for b, into the general equation y = ab^x gives:
y = 6(5/2)^x So that is the answer. :)