Question 1130384
a)construct a table of values for the exponential function {{{y=2(3)^x }}}
Use values of {{{x}}} from {{{-1}}} to {{{3}}}.


{{{x}}}|{{{y}}}
{{{-1}}}|{{{2/3}}}->{{{y=2(3)^-1=2*(1/3)=2/3 }}}
{{{0}}}|{{{2}}}->{{{y=2(3)^0=2*1=2 }}}
{{{1}}}|{{{6}}}->{{{y=2(3)^1=2*3=6 }}}
{{{2}}}|{{{18}}}->{{{y=2(3)^2=2*9=18 }}}
{{{3}}}|{{{54}}}->{{{y=2(3)^3=2*27=54}}}


b) Graph the equation. Connect the points with a solid line.

{{{drawing (600,600, -10, 10, -10, 55,
circle(-1,2/3,.2),circle(0,2,.2),circle(1,6,.2),circle(2,18,.2),circle(3,54,.2),
graph(600,600, -10, 10, -10, 55,2(3)^x,0 )) }}} 



c) What is the x-intercept? What is the y-intercept?

set {{{y=0}}} to find the x-intercept

{{{0=2(3)^x }}}...(no solutions exist)=> there is no x-intercept

set {{{x=0}}} to find the y-intercept
{{{y=2(3)^0 }}}->{{{y=2*1 }}}->{{{y=2}}}
the y-intercept is at ({{{0}}},{{{2}}})


d) What is the asymptote?

{{{y = 2*3^x }}}is asymptotic to {{{y = 0}}}


e) Using the graph, estimate the value of {{{x}}} when {{{y=18 }}}


 {{{y=18 }}} is approximately where  {{{x=2}}}