Question 134605
Use Logs
Given:{{{y=ab^x}}}
{{{Log(y) = Log(a) + xLog(b)}}}
{{{Log(y) - xLog(b) = Log(a) }}}

Sub in both sets of points. Since Log(a) is the same in both equations, we can set them equal to each other.

{{{Log(3) - 4Log(b) = Log(4.5) - 9Log(b)}}}
{{{Log(3) - Log(4.5) = -5Log(b)}}}
{{{(0.477 - 0.653)/-5 = Lob(b)}}}
{{{0.035218 = Log(b)}}}
{{{10^0.035218 = b}}}
{{{1.0845 = b}}}

Now solve for a 
{{{3 = a*(1.0845)^4 }}}
{{{3/1.383 =a}}}

Function is:
{{{y = 2.169 * 1.0845^x }}}

Verify the function by plugging in the given points