A bus that costs $42,000 when new depreciates according to the exponential model, V=42000e^(-.3t) After how many years will the bus be worth 20,000

Question

A bus that costs $42,000 when new depreciates according to the exponential model, V=42000e^(-.3t) After how many years will the bus be worth 20,000

Answer 1

V = 42000e^-0.3t

20000 = 42000e^-0.3t

10/21 = e^-0.3t

0.476 = e^-0.3t

ln 0.476 = ln e^-0.3t

ln 0.476 = -0.3t ln e

ln 0.476 = -0.3t

-0.742 = -0.3t

2.473 = t

 

After 2.47 years the bus shall be worth $20,000.