Write an exponential function y = abx for a graph that passes through (2, 1) and (3, 8).

Question

Write an exponential function y = ab^x

 for a graph that passes through (2, 1)

 and (3, 8).

Answer 1

y = ab^x

Since (2,1) is on the graph, 1 = ab²

Since (3,8) is on the graph, 8 = ab³

From the first equation, a = 1/b²

Substituting into the equation 8 = ab³, we have 8 = (1/b²)b³. So, b = 8.

a = 1/b² = 1/64

Therefore, y = (1/64)(8^x)

Answer 2

2= ab

8= ab^3= ab*b^2

8= 2b^2 <--- substitutes ab=2

4=b^2

B=2

Which forces a=1

Y= 2^x