An automated trading algorithm is monitoring the growth of a digital asset portfolio. The value of the portfolio, VVV pounds, at time ttt weeks after the algorithm was activated is modelled by the equation
log10V=1.94+0.12t \log_{10} V = 1.94 + 0.12t log10V=1.94+0.12tWrite this equation in the form V=abtV = ab^tV=abt, where aaa and bbb are constants to be found. Give each value to 4 significant figures.
When t=Tt = Tt=T, the value of the portfolio is £4000. Find the value of TTT according to the model, giving your answer to 3 significant figures.
The algorithm is programmed to trigger a 'rebalance' alert if the portfolio value exceeds £5000. Determine whether or not the portfolio will require a rebalance within the first 14 weeks.
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.