Question 1
Paper 1Medium14 marksA horticulture centre monitors the depth of water in a shallow pond during a controlled fill-and-drain test. Let be the time, in hours, since the test began, and let be the depth of water, in centimetres.
| 0 | 2 | 5 | 7 | |
|---|---|---|---|---|
| 1.3 | 7.6 | 10.1 | 7.0 |
Choose the most suitable model from a linear, quadratic or exponential model for these data. Justify your choice.
Using only the observations at and fit a quadratic model of the form Show that
where the coefficients are given to 3 significant figures. Retain unrounded values for later parts.
Use your fitted model to estimate the depth at Compare your estimate with the recorded depth.
Use your fitted model to estimate the time at which the depth is cm on the falling part of the curve. Give your answer to the nearest hour.
State a reasonable domain for using this model, based on the observations. Use the model to estimate the depth at and comment on whether this prediction is reasonable.