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1 Unit 1: Pure Mathematics A

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Question 45

The concentration of a drug (C C\,C mg/L) in a patient's bloodstream t t\,t hours after administration is recorded in the table below.

ttt1246810
CCC26.319.110.05.22.81.4

The data is coded using the changes of variable x=tx = tx=t and y=log⁡10Cy = \log_{10} Cy=log10​C.

The regression line of y y\,y on x x\,x is found to be y=1.56−0.14xy = 1.56 - 0.14xy=1.56−0.14x.

a.

Given that the data can be modelled by an equation in the form C=abtC = ab^tC=abt where a a\,a and b b\,b are constants, find the values of a a\,a and b b\,b to 3 significant figures.

[3]
b.

Give an interpretation of the constant a a\,a in this equation.

[1]
c.

Explain why this model might not be reliable for calculating the concentration after 72 hours.

[1]
Markscheme

1 Unit 1: Pure Mathematics A Questions

  1. A Level
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