Question 1156098
Find an exponential function of the form

{{{f(x) = ba^(-x) + c}}}

that has the given horizontal asymptote and y-intercept and passes through point P.

{{{y = 34}}};

 y-intercept {{{659}}};=> ({{{0}}}, {{{569}}})

A function of the form {{{f(x) = a (bx) + c }}}always has a horizontal asymptote at {{{y = c}}}

=> if given {{{y = 34}}}, then {{{c=34}}}

{{{f(x) = ba^(-x) +34}}}


use P({{{2}}}, {{{134}}}) and  {{{c=34}}}


{{{569 = ba^-0 + 34}}}
{{{569 -34= b }}}
{{{b=535}}}

so far

{{{f(x) = 535a^(-x) +34}}}.......=> use given point ({{{2}}},{{{134}}})

{{{134= 535a^(-2)+34}}}

{{{134-34 = 535/a^2 }}}

{{{100 = 535/a^2 }}}

{{{a^2 = 535/100 }}}

{{{a^2 = 5.35 }}}

{{{a =sqrt( 5.35 )}}}

{{{a=2.31301}}}


your function is:


{{{f(x) = 535(2.31301)^(-x) +34}}}