Question 1137333
Find the exponential function {{{f=ca^x}}} whose graph goes through the points ({{{0}}},{{{3}}}) and ({{{2}}},{{{12}}})?
{{{a}}}=
{{{c}}}=


{{{f=ca^x}}}....use  the points ({{{0}}},{{{3}}})

{{{3=ca^0}}}
{{{3=c*1}}}
{{{c=3}}}

{{{f=3a^x}}}....use  the points ({{{2}}},{{{12}}})

{{{12=3a^2}}}

{{{12/3=a^2}}}

{{{a^2=4}}}

{{{a=sqrt(4)}}}

{{{a=2}}} 

{{{f=3*2^x}}}




check: {{{f=3*(2)^x}}}

{{{ drawing( 600, 600, -10, 10, -10, 15,
circle(0,3,.12),locate(0,3,p(0,3)),
circle(2,12,.12),locate(2,12,p(2,12)),
 graph( 600, 600, -10, 10, -10, 15,3 (-2)^x ,3*(2)^x)) }}}