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. This function is actually representing an exponential decrease in value by 40% every year, rather than every two years as stated in the problem.
To correct this, we need to adjust the function to represent a decrease in value by 40% every two years. We can do this by adjusting the exponent in the function.
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/2
This function takes into account the fact that the value of the equipment is reduced by 40% every two years.