exponential model y=y0e^kt

Question

a company buys a machine for $20 million. Four years later, the machine is worth $12 million. Assume the decline in value follows the exponential model y=y0e^kt. Find the exponential model. Use the model to determine the machine's value in another two years.

Answer 1

y0 = 20

y = 12

t = 4

Find k

 

12 = 20 * (e^k*4)

12/20 = e^k*4

ln(12/20) = k4

-0.511 = k*4

k = -0.1277