Question 730922
given:

{{{y=ab^x}}} whose graph passes through the points of 

({{{-1}}},{{{ 48}}}) and ({{{2}}}, {{{6}}})

Make a system of equations with the points by substituting them for {{{x}}} and {{{y}}}:

{{{48 = ab^(-1)}}}.........1
{{{6 = ab^2}}}.................2

{{{48 = a(1/b)}}}.........1
{{{6 = ab^2}}}.................2

take

{{{48 = a(1/b)}}}.........1 and solve for {{{a}}} 

{{{48b= a}}}..........substitute in {{{2}}}

{{{6 = (48b)b^2}}}.................2 solve for {{{b}}}

{{{6 = 48b^3}}}

{{{6/48 = b^3}}}

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

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

{{{root(3,1)/root(3,2^3) = b}}}

{{{b=1/2}}}

now find {{{a}}}

{{{a = 48(1/2)}}}

{{{a = 48/2}}}

{{{a=24}}}

The exponential function is {{{y = 24(1/2)^x}}}.


{{{ drawing(600, 600, -6, 5, -10, 55,circle(-1,48,0.1),circle(2,6,0.1),graph( 600, 600, -6, 5, -10, 55, 24(1/2)^x)) }}}