Question 770811
find a function defined by {{{f(x) = ab^x}}}

if given {{{f(0)= 13.1}}}, means for {{{x=0}}} => {{{f(x)= 13.1}}}; so, you will have   

{{{13.1 = ab^0}}}....since {{{b^0=1}}}

{{{highlight(13.1 = a)}}}

now we can use given {{{f(7) = 17.4}}} to find {{{b}}}

{{{17.4 = 13.1b^7}}}

{{{17.4/13.1=b^7}}}

{{{1.33=b^7}}}

{{{b=root(7,1.33)}}}

{{{b=1.041581}}}

{{{highlight(b=1.0415)}}}


so, your function is: {{{f(x) = 13.1(1.0415)^x}}}



*find a function defined by {{{g(x) = cd^x}}} do this one same way

if {{{f(0) = 4.9}}} => {{{4.9 = cd^0}}} => {{{highlight(c=4.9)}}}   

now find {{{d}}}

{{{F(7) = 8.7}}}=> {{{8.7 = 4.9*d^7}}} => {{{8.7/4.9 = d^7)}}} => {{{1.78 = d^7)}}} => {{{root(7,1.78) = d)}}} =>{{{highlight(d=  1.0858)}}}


{{{g(x) = 4.9(1.0858)^x}}}