Given: A exponential function-
[tex]y=a\cdot b^x[/tex]
passing through the points (1,6) and (2,9)
Required: To find out the value of a and b.
Explanation: Since the given exponential function is passing through (1,6)
[tex]6=a\cdot b^1\text{ ..........\lparen1\rparen}[/tex]
Now the function is also passing through (2,9)
[tex]9=a\cdot b^2\text{ ......\lparen2\rparen}[/tex]
Dividing eq 2 and eq 1 we get,
[tex]\frac{9}{6}=\frac{a\cdot b^2}{ab^}[/tex][tex]\frac{3}{2}=b[/tex]
Putting this value of b in eq 1,
[tex]6=a\times\frac{3}{2}[/tex]
This gives,
[tex]a=4[/tex]
Final answer: The value of a=4 and b=1.5
