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1.6 Exponentials and Logarithms

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Question 57

A chemical engineer is studying the rate at which a specific solid reactant dissolves in a solvent. The mass of the remaining reactant, MMM grams, is recorded hhh hours after the process begins. The relationship is modelled by the equation

log⁡10M=−0.0583h+1.9030≤h≤24 \log_{10} M = -0.0583h + 1.903 \quad 0 \le h \le 24 log10​M=−0.0583h+1.9030≤h≤24
a.

Show that this equation may be written in the form

M=abh M = ab^h M=abh

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

[4]
b.

Use the model to predict the mass of the reactant remaining after 24 hours. Give your answer to 2 significant figures.

[2]

1.6 Exponentials and Logarithms Questions

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