The population of a bacterial colony, PPP, is being monitored in a laboratory. The number of bacteria is modelled by the equation
log10P=2+0.04t \log_{10} P = 2 + 0.04t log10P=2+0.04twhere t t\,t is the time in hours after monitoring began.
Use the equation of the model to answer parts (a) and (b).
Find the initial population of the bacterial colony.
After T T\,T hours, the population reaches 500. 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.