Linear, quadratic, and exponential

Question

These data show the mass of algae in a pond during summer changes over time.

Time (s) 5 10 15 20 25 30

Mass (kg) 4.4 5.2 6.6 8.4. 10.8 13.6

a) Perform linear, quadratic, and exponential regressions on the data.

b) Which model best represents the data? Justify your answer.

Answer 1

If you put the data set into Excel and run a regression analysis.

Linear Regression:

Exponential Regression:

Quadratic Polynomial Regression:

The R²=0.9999 for the polynomial regression analysis is the highest among linear and exponential regression analyses.

Therefore it is the best fit is the quadratic regression.

Answer 2

Look at the time pattern and the mass pattern. I am able to predict that the graph is linear.