Tucker purchased $4,600 in new equipment for a catering business. He estimates that the value of the equipment is reduced by app
roximately 40% every two years. Tucker states that the function V(t)=4,600(0.4)2t could be used to represent the value of the equipment, V, in dollars, t, years after the purchase of the new equipment. Explain whether the function Tucker stated is correct, and, if not, determine the correct function that could be used to find the value of the equipment purchased.
Answer: The function stated by Tucker is incorrect. V(t) = 4600(0.8)^t Step-by-step explanation: Given the function : V(t)=4,600(0.4)2t The initial value of equipment = 4600 Decay rate = 40% of very 2 years The value of equipment t years after purchase The exponential decat function goes thus : V(t) = Initial value * (1 - decay rate)^t The Decay rate per year = 40% /2 = 20% = 0.2 V(t) = 4600(1 - 0.2)^t V(t) = 4600(0.8)^t