Question 72913
Plug in both x and y into the general form
{{{y=ab^x}}}
{{{4=ab^1}}}Plug in (1,4)
{{{b=4/a}}}solve for b
{{{12=ab^2}}}Plug in point (2,12)
Now plug in b=4/a into b of {{{12=ab^2}}}
{{{12=a(4/a)^2}}}
{{{12=a(16/a^2)}}}
{{{12=16/a}}}Solve for a
{{{a=16/12}}}
{{{a=4/3}}}Plug this into {{{y=ab^x}}} with any point also
{{{4=(4/3)b^1}}}Solve for b
{{{4(3/4)=b}}}
{{{b=3}}}
So the equation is 
{{{y=(4/3)(3)^x}}}
Check:
Plug in x=1, you should get y=4
{{{y=(4/3)(3)^1}}}
{{{y=4}}}works
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Plug in x=2, you should get y=12
{{{y=(4/3)(3)^2}}}
{{{y=(4*9)/3}}}
{{{y=12}}}works