Exponential function from two points.

Question

 Write an exponential equation in y = ab^x form. Points are (0, 0.2) and (1, 1.6). Please help!

Answer 1

y=ab^x

 

(0, 0.2) : 0.2=ab⁰ 

(1, 1.6): 1.6=ab¹

a=0.2

ab=1.6

b=1.6/0.2=8

 

The function is y=0.2*8^x

or you can write as  (1/5)8^x=8^x/5

 

 

Answer 2

y = a(b)^x

 

Since (0, 0.2) is on the graph, 0.2 = a(b)⁰.  So, a = 0.2.

 

y = 0.2(b)^x

 

Since (1, 1.6) is on the graph, 1.6 = 0.2(b)¹

 

                                            1.6 = 0.2b     b = 8

 

Therefore, y = 0.2(8)^x.