Question

A 2005 Jeep Wrangler that costs $30,788 new has a book value of $18,000 after 2 years.
a.) Find the exponential model V= ae^kt

Answer 1

Please help me!!!

Answer 2

ok I figured it out

Answer 3

first plug in all your values
A=Initial
V=Final
k=?
t=2

Answer 4

\[18000=30788e ^{2k}\] \[\frac{ 18000 }{ 30788 }=\frac{ 30788e ^{2k} }{ 30788 }\] \[.585=e ^{2k}\]

Answer 5

now to get rid of e we take the natural log of both sides \[\ln .585=\ln e ^{2k}\] \[-.536=2k\] then divide both sides by 2 and you get \[-.268=k\]

Answer 6

when you plug it in you get approximately 18,000. You actually get 18,013.56 but that's only because I rounded some of the numbers off .585, -.536,and -.268