The market value VVV, in pounds (£), of a limited-edition bronze sculpture is modelled by the equation
V=pqt V = pq^t V=pqtwhere 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 log10V\log_{10} Vlog10V 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).
Determine an equation for this line in the form log10V=mt+c\log_{10} V = mt + clog10V=mt+c.
Calculate the value of ppp and the value of qqq, giving your answers to 3 significant figures.
Use the model to estimate the number of years, ttt, until the sculpture reaches a value of £50,000.
Practise Edexcel A Level Maths Exponential Models with exam-style questions for A Level Maths. 42 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
