Question

A hurricane is predicted to hit the coast in 5 days. Supplies are expected to dwindle as people prepare. The manager of the hardware store has 8200 square feet of plywood the day the storm was announced. He projects the daily supply to be 4100 square feet, 2050 square feet, and 1025 square feet over the next 3 days. What type of function model the scenario? Choose from linear, exponential growth, and exponential decay. Explain your reasoning.

Answer 1

To test if linear model, we fit the data into a line and solve for the correlation coefficient:
The equation is
y = -1537.5x + 5466.67
and the correlation coefficient is
R² = 0.964

The model can't be exponential growth since the daily supply decreases with time. So, the data is tested if it's exponential decay. The same procedure is done the exponential equation would be linearized in the form:
y = -2816.06 lnx + 4073.57
with correlation coefficient of
R² = 0.998

Since the correlation coefficient for the exponential decay model is closer to 1, it must be the right model.