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 A Level Maths 1.6 Exponentials and Logarithms, covering 1.6.1 Properties of the exponential function, 1.6.2 Gradient of e^(kx) (A-level only), 1.6.3 Definition of the logarithm, 1.6.4 The natural logarithm function, 1.6.5 ln x as inverse of e^x, 1.6.6 Laws of logarithms, 1.6.7 Equations involving exponentials, 1.6.8 Reduction to linear form, and 1.6.9 Modelling using exponential functions. Each one has a worked solution and a mark scheme showing where the marks go.