A certain piece of machinery was purchased 5 yr ago by Garland Mills for $470,000. Its present resale value is $280,000. Assuming that the machine's resale value decreases exponentially, what will it be 3 yr from now? $___________.thanks
decreases exponentially: A_t = A_0 e^(kt) A_0 = original value A_t = value at time t t = time elapsed from original value k = coefficient of growth/decay (or something like that) e = 2.718... using time, your original value, and current value, find k. from there, find A_t three more years down the road. units don't matter as long as they're consistent. and, your answer should make sense according to the context; i.e. less than $280000. hope this helps
Sine the price decreases exponentially, we can model this with: A = P*e^(kt). Since the initial value is $470k, we have P = 470000 and so the equation becomes: A = 470000e^(kt). Since the value 5 years after purchasing it is $280k, we have: 280000 = 470000*e^(5k) == e^(5k) = 28/47 == 5k = ln(28/47) == k = ln(28/47)/5 ≈ -0.1035886. Thus, the price after t years is 470000e^(-0.1035886t) and so the price 3 years later (8 years after buying) is: A = 470000e^[(-0.1035886)(8)] ≈ $205,208. I hope this helps!
