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1.6.8 Exponentials and logarithms

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Question 39

The market value VVV, in pounds (£), of a limited-edition bronze sculpture is modelled by the equation

V=pqt V = pq^t V=pqt

where ttt is the number of years since its initial release and ppp and qqq are constants.

A researcher records the market value over several years. The graph of log⁡10V\log_{10} Vlog10​V against ttt is a straight line that passes through the points (0,3.15)(0, 3.15)(0,3.15) and (12,5.07)(12, 5.07)(12,5.07).

a.

Determine an equation for this line in the form log⁡10V=mt+c\log_{10} V = mt + clog10​V=mt+c.

[2]
b.

Calculate the value of ppp and the value of qqq, giving your answers to 3 significant figures.

[3]
c.

Use the model to estimate the number of years, ttt, until the sculpture reaches a value of £50,000.

[2]

1.6.8 Exponentials and logarithms Questions

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