IB Maths AI HL AI 2.2 Modelling questions

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Question 1

Paper 1Medium7 marks

A website records the number of visits per day during the first five days after its launch.

$t$ number of days after launch	1	2	3	4	5
$V$ visits per day	320 000	470 000	760 000	1 040 000	1 700 000

To work with more manageable values, let $W=V/100\,000$ The manager considers an exponential model $W=A b^{t-1}$ and a power model $W=Ct^p$

(a)

For the exponential model, determine the fitted values of $A$ and $b$ and the Pearson’s product moment correlation coefficient for the linearized data. Give your answers to three significant figures.

[3]

(b)

For the power model, determine the fitted values of $C$ and $p$ and the Pearson’s product moment correlation coefficient for the linearized data. Give your answers to three significant figures.

[3]

(c)

State which model is better supported by these data, giving a reason based on the correlation coefficients.

[1]

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