The growth of a specialized digital database is being tracked. The total amount of data stored, DDD terabytes (TB), at time ttt years after the system went online is modelled by the equation
log10D=0.65+0.42t \log_{10} D = 0.65 + 0.42t log10D=0.65+0.42tWrite this equation in the form D=pqtD = pq^tD=pqt, where ppp and qqq are constants to be found. Give each value to 4 significant figures.
When t=Tt = Tt=T, the amount of data stored is 350 TB. Find the value of TTT according to the model, giving your answer to 3 significant figures.
The current hardware infrastructure can accommodate a maximum of 2,000 TB. Determine whether or not the data volume will exceed this limit within the first 6 years of the study.
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.