9758/2021/P2/Q09

In a chemical reaction the mass, $x$ grams, of a particular product at time $t$ minutes is given in this table.

The value of the product moment correlation coefficient is $0.9803$ correct to 4 significant figures. The scatter diagram for the data is shown below.

(a) Toby attempts to model the relationship between $x$ and $t$ with a straight line. Explain whether this is likely to provide a good model.

[1]

Toby now tries a model in which $x$ has been transformed to $\ln x$.
(b) (i) Sketch a scatter diagram of $\ln x$ against $t$ for the data given in the table.

[1]

(ii) Toby models the data with the equation $\ln x=c+d t$. Find the values of the constants $c$ and $d$ and state the value of the product moment correlation coefficient for this model.

[3]

(c) Comment on Toby’s two models.

[2]