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.
104 exam-style questions on OCR (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.