Question

The decreasing number of wolves in the northern section of the Southern Isles is represented by the function p(t) =80 (0.965)t. In the function p(t), explain what 80 and 0.965 represent.

a) 80 represents the initial number of wolves, and 0.965 represents the growth factor.
b) 80 represents the maximum number of wolves, and 0.965 represents the decay factor.
c) 80 represents the initial number of wolves, and 0.965 represents the rate of decrease.
d) 80 represents the carrying capacity, and 0.965 represents the birth rate.

Answer 1

In the function p(t), 80 represents the initial number of wolves in the southern isles, and 0.965 is the decay factor, signifying the rate at which the population decreases over time.

Step-by-step explanation:

In the function p(t) = 80 (0.965)t, the number 80 represents the initial number of wolves in the southern isles. It's the population size at the beginning of the observation or at time t = 0. The number 0.965 is the decay factor. This factor represents the rate at which the number of wolves is decreasing each time interval (usually annually). Since the decay factor is less than one, it indicates that the wolf population is decreasing, rather than increasing.

Therefore, the correct answer is option b) 80 represents the maximum number of wolves, and 0.965 represents the decay factor, as it indicates a decreasing wolf population over time.