Question 197691
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The increasing rate of Gold Coin follows:
{{{P+P*Rate(n)=F}}}, where{{{system(P=9000,Rate=0.0179/yr,red(n=years),F=17978.02)}}}


Substituting:
{{{9000+(9000)(0.0179)(red(n))=17978.02}}}
{{{161.10*(red(n))=17978.02-9000}}}
{{{cross(161.10)*red(n)=(17978.02-9000)/161.10=8978.02/161.10}}}
{{{highlight(red(n=55.73yrs))}}}, let us say <font color=blue>56 years</font>



*One good way to check on this is by graphing.


Let us appoint the following:
{{{x=red(years)}}} & {{{y=red(Price)}}}
It follows,{{{system(x[1]=0,y[1]=9000,x[2]=55.73,y[2]=17978.02)}}}
Via Point Slope Form,
{{{m=(y[2]-y[1])/(x[2]-x[1])=(17978.02-9000)/(55.73-0)=8978.02/55.73}}}
{{{red(m=161.10)}}}


 Thru point {{{x[1]}}} & {{{y[1]}}}, (0,9000)
{{{y=mx+b}}}, Slope-Intercept Form
{{{9000=(161.10)(0)+b}}}
{{{9000=0+b}}}
{{{b=9000}}}, Y-Intercept


It follows ---> {{{red(y=(161.10)x+9000)}}}, Line Eqn

{{{drawing(500,500,-10,65,-500,20000,graph(500,500,-10,65,-500,20000,161.10x+9000),green(line(0,17978.02,55.73,17978.02)),green(line(55.73,17978.02,55.73,0),red(locate(56,700,55.73yrs)),red(locate(4,18600,17978.02)),green(arrow(34,14150,38,13030)),green(locate(33,12500,y=161.10(x)+9000)),red(locate(18,700,YEARS)),green(circle(0,9000,.35)),green(circle(0,9000,.55)),green(circle(0,9000,.75)),green(locate(2,9000,Yintercept))))}}}




Thank you,
Jojo</font>