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1.8 Exponentials and Logarithms

1.8 Exponentials and Logarithms

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Question 74

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

log⁡10D=0.65+0.42t \log_{10} D = 0.65 + 0.42t log10​D=0.65+0.42t
a.

Write 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.

[3]
b.

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.

[2]
c.

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.

[2]
Markscheme

1.8 Exponentials and Logarithms Questions

  1. A Level
  2. /Maths
  3. /1.8 Exponentials and Logarithms

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.

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