Question

The population of a colony of ants has been observed by a group of scientists. The equation p= 5000(4/5)^m gives the population of ants, p, m months since the scientist began observing the colony. Explain what the numbers 5000 and 4/5 represent in this situation.

Answer 1

The 5000 in the equation is the initial ant population, and the 4/5 represents the monthly population decay factor, with the population decreasing to 80% of its size each month.

Step-by-step explanation:

The equation p = 5000(4/5)^m describes the population of a colony of ants, where p represents the population and m represents the number of months since the observation began. In this context, the number 5000 is the initial population of the colony at the start of observation, which acts as the starting value in the exponential decay function. The fraction 4/5 represents the decay factor, which shows that the population of ants decreases to 80% (or four-fifths) of its size every month, indicating a consistent rate of decline over time.