Question 1197442


 Find the equation for an exponential function that passes through the pair of points given below. (Round all coefficients to four decimal places when necessary.)


An exponential function is defined by the formula 

{{{f(x) = a*b^x}}}

if   passes through ({{{-1}}}, {{{-4}}}) , we have

{{{-4 = a*b^-1}}}

{{{-4 = a*1/b}}}

{{{a= -4 b}}}..........eq.1

and ({{{2}}}, {{{-0.5}}}), we have

{{{-0.5 = a*b^2}}}

{{{a=-(1/2)/b^2}}}

{{{a=-1/(2b^2)}}}............eq.2


{{{ -4 b=-1/(2b^2)}}}.

{{{ -4 b*2b^2 =-1}}}

{{{ -8b^3 =-1}}}

{{{ b^3 =-1/-8}}}

{{{ b =root(3,1/8)}}}

{{{b=1/2}}}  


then
{{{a= -4 (1/2)}}}..........eq.1

{{{a= -2}}}

your equation is:

{{{f(x) = -2*(1/2)^x}}}


{{{ drawing( 600, 600, -10, 10, -10, 10,
circle(-1,-4,.12), locate(-1,-4,p(-1,-4)),
circle(2,-0.5,.12), locate(2,-0.5,p(2,-0.5)),
graph( 600, 600, -10, 10, -10, 10, -2*(1/2)^x )) }}}