Question 1157787
Write the exponential equation passing through the points ({{{3}}},{{{ 8}}}) and ({{{7}}}, {{{58}}}).


{{{f(x)=a*b^x}}}......use first point

{{{8=a*b^3}}}

{{{a=8/b^3}}}.....eq.1



{{{58=a*b^7}}}......use second point

{{{a=58/b^7}}}.....eq.2

from eq.1 and eq.2 we have


{{{8/b^3=58/b^7}}}

{{{b^7/b^3=58/8}}}

{{{b^4=58/8}}}

{{{b^4=29/4}}}

{{{matrix(2,1,"",b=29^(1/4)/sqrt(2))}}}  
   


{{{matrix(2,1,"",a=8/((29/4)^(1/4)/sqrt(2))^3)}}}.....eq.1


{{{matrix(2,1,"",a=(16sqrt(2))/29^(3/4))}}}



your exponential equation is:


{{{matrix(2,1,"",f(x)=((16sqrt(2))/29^(3/4))*(29^(1/4)/sqrt(2))^x)}}}