Here's the question you clicked on:
haleyking345
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
first plug in all your values A=Initial V=Final k=? t=2
\[18000=30788e ^{2k}\] \[\frac{ 18000 }{ 30788 }=\frac{ 30788e ^{2k} }{ 30788 }\] \[.585=e ^{2k}\]
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 \[-.268=k\]
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