Question 736514
 an exponential function of the form {{{y=ab^x}}} whose graph passes through the given points ({{{0}}},{{{2}}}),({{{-6}}},{{{17}}}) you can find if you find first what {{{a}}} and {{{b}}} is equal to

plug in given points in {{{y=ab^x}}} and find {{{a}}} 

{{{y=ab^x}}}.......if ({{{x=0}}},{{{y=2}}}), then

{{{2=ab^0}}}

{{{2=a*1}}}

{{{2=a}}}

now find {{{b}}}


{{{y=ab^x}}}.......if ({{{x=-6}}},{{{y=17}}}), and {{{2=a}}}, then

{{{17=2b^-6}}}

{{{17=2(1/b^6)}}}

{{{17b^6=2}}}

{{{b^6=2/17}}}

{{{b^6=0.118}}}

{{{b=root(6,0.118)}}}

{{{b=0.7003476}}}....round it

{{{b=0.7}}}

so, your exponential function is: {{{y=2*0.7^x}}}


{{{ drawing( 600, 600, -10, 10, -10, 20,circle(0,2,0.2),circle(-6,17,0.2),graph( 600, 600, -10, 10, -10,20, 2*0.7^x)) }}}