Question

The game commission introduces 200 white-tailed deer into a newly acquired national game and wildlife park. The population of the herd is modeled by the graph of the rational function below, where time is measured in years.
mc027-1.jpg
Which statement about the population is true?
The graph shows that the population of deer will eventually be 0.
The rate at which the population of deer grows decreases as it approaches 1,500.
The graph shows that the population of deer decreases over time.
The rate at which the population of deer grows increases as it approaches 1,500.

Answer 1

The rate at which the population of deer grows decreases as it approaches 1,500.

Reason: the graph starts at 200 and increases toward a horizontal asymptote at y = 1,500, so the population is rising but the slope (growth rate) gets smaller as the curve flattens near 1,500. The population does not go to 0, nor does it decrease over time, and the growth rate does not increase as it approaches 1,500.