The surface area SSS, in mm2\text{mm}^2mm2, of a metallic crystal growing in a laboratory environment is monitored over time. The surface area is modelled by the equation
log10S=0.85+0.072t \log_{10} S = 0.85 + 0.072t log10S=0.85+0.072twhere t t\,t is the time in hours after the crystal began to form.
Use the equation of the model to answer parts (a) and (b).
Find the initial surface area of the crystal, giving your answer to 2 decimal places.
After T T\,T hours, the surface area reaches 120 mm2. Find the value of TTT, giving your answer to 2 decimal places.
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.