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1.6.8 Reduction to linear form

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Question 26

A scientist is studying the growth of a synthetic crystal in a laboratory. The mass of the crystal, MMM grams, recorded ddd days after the growth process began, is modelled by the equation

log⁡10M=0.0607d+1.1760≤d≤20 \log_{10} M = 0.0607d + 1.176 \quad 0 \le d \le 20 log10​M=0.0607d+1.1760≤d≤20
a.

Show that this equation may be written in the form

M=abd M = ab^d M=abd

where aaa and bbb are constants to be found. Give the value of aaa to the nearest integer and give the value of bbb to 3 significant figures.

[3]
b.

Use the model to predict the mass of the crystal 20 days after the growth process began. Give your answer to 2 significant figures.

[2]

1.6.8 Reduction to linear form Questions

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