Tucker purchased $4,600 in new equipment for a catering business. He estimates that the value of the equipment is reduced by approximately 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.(4 points)
The function Tucker stated, V(t)=4,600(0.4)^2t, is not correct. The correct function to represent the value of the equipment, V, in dollars t years after the purchase of the new equipment would be:
V(t) = 4,600*(0.6)^t
This is because the value of the equipment is reduced by 40% every two years, so after t years, the equipment would retain 60% of its original value. The exponential decay function above accurately represents this decrease in value over time.