Question

Olivia is tracking the growth rate of a population of termites, x, living in a mound. When the population is x = 400, it is the 0th hour. Initially, it takes f(x) = 1 hour for the population to grow by 400 termites. When the population grows by another 400 termites, the total time taken is f(x) = 1.585 hours. The time taken keeps decreasing to model the same incremental growth. Does the equation for f(x) or the graph of g(x) correctly model the situation?

Answer 1

Based on the information in the problem statement, the function must pass through points (400 , 0), (800 , 1), and (1,200 , 1.585). Notice that the graph of function g(x) passes through these points.

Next, check the graph of f(x). Plot the function using the given equation to see which points it passes through.

The equation indeed starts at (400 , 0), but it doesn’t pass through the other two required points. So, the graph of g(x) fits the situation, but the equation for f(x)does not.