The trees in a forest are being cut down at a monthly rate of 3.2%. This situation can be modeled by an exponentia function. The forest contained 5,500 trees when cutting began. Which function can be used to find the number of trees in the forest at the end of m months?
A) t(m) - 5,500(0.032)m
B) t(m) - 5,500(1.968)m
C) t(m) -5,500(1.032)m
D) t(m) -5,500(0.968)m
To model the decay of the number of trees in the forest as an exponential function, you need to consider the rate at which the trees are being cut down. A 3.2% monthly reduction rate means that 96.8% (100% - 3.2%) of the trees remain after each month.
The formula to calculate the number of trees after m months would be:
t(m) = initial number of trees * (percentage remaining after each month)^m
Turning the percentage remaining into a decimal, we get 96.8% = 0.968. Therefore, the formula becomes:
t(m) = 5500 * (0.968)^m
Hence, the correct function is:
D) t(m) = 5500 * (0.968)^m