## haleyking345 Group Title 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 one year ago one year ago

1. haleyking345 Group Title

2. MATTW20 Group Title

ok I figured it out

3. MATTW20 Group Title

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

4. MATTW20 Group Title

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

5. MATTW20 Group Title

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 $-.268=k$

6. MATTW20 Group Title

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