Question 1179585


 {{{V = 250000e^(an)}}}

 When {{{n = 3}}}, {{{V = 350000}}}

Finde the initial value of this house. Find the value of a. 

 {{{350000= 250000e^(a*3)}}}

 {{{350000/250000=e^(a*3)}}}

 {{{7/5=e^(a*3)}}}............take ln of both sides

{{{ln(7/5)=ln(e^(a*3))}}}

{{{ln(7/5)=(a*3)ln(e)}}}

{{{3a=ln(7/5)/ln(e)}}}..............ln(e)=1

{{{3a=ln(7/5)}}}

{{{a=(ln(7)-ln(5))/3}}}

{{{a=0.1122}}}

Estimate the number of years for this house to double in value.

{{{2*350000= 250000e^(0.1122*n)}}}

{{{700000/250000=e^(0.1122*n)}}}

{{{14/5=e^(0.1122*n)}}} ...........take ln of both sides

{{{ln(14/5)=ln(e^(0.1122*n))}}}

{{{ln(14)-ln(5)=(0.1122*n)ln(e)}}}

{{{ln(2*7)-ln(5)=(0.1122*n)*1}}}

{{{ln(2)+ln(7)-ln(5)=0.1122*n}}}

{{{1.0296194171811581=0.1122*n}}}

{{{n=1.0296194171811581/0.1122}}}

{{{n=9.18}}}

this house will double in value in {{{9.18}}} years