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

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

anonymous · Answer

Please help me!!!

anonymous · Answer

ok I figured it out

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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 $$-.268=k$$

anonymous · Answer

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