Final answer:
The function that models the number of trees remaining after m months of a constant 3.2% monthly decrease from an initial 5,500 trees is D. t(m) = 5,500(0.968)m, which represents exponential decay.
Step-by-step explanation:
To determine the function that can be used to find the number of trees in the forest at the end of m months, given that the trees are being cut down at a monthly rate of 3.2%, we need to consider the nature of exponential decay. An exponential decay model has the form N(t) = N0e-kt, where N0 is the initial amount, k is the decay rate, and N(t) is the amount at time t. Here, N0 is 5,500 trees, and the trees are being cut at a rate of 3.2%, which means that after each month, we have 100% - 3.2% = 96.8% of the trees left, or 0.968 of the original number. Hence, the appropriate model for the number of trees left after m months is obtained by multiplying the initial number of trees by 0.968 to the power of m, signifying multiple periods (months) of decay at this constant rate.
The correct function is therefore D. t(m) = 5,500(0.968)m. Option D reflects the monthly decay rate subtracted from 1, which is typical for decay processes modeled by exponential functions.