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1.8 Exponentials and Logarithms

1.8 Exponentials and Logarithms

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Question 20
37%

The temperature of water in a kettle is modelled using the formula T=75e−kt+22T = 75e^{-kt} + 22T=75e−kt+22 Where T T\,T is the temperature t t\,t minutes after the kettle is turned off and k k\,k is a positive constant.

a.

Find the rate of change of the temperature in terms of kkk

[2]
b.

After 5 minutes the temperature of the water is 70∘C70^{\circ}\text{C}70∘C. Find the value of kkk

[3]
c.

Find how many minutes it takes for the water to cool to 55∘C55^{\circ}\text{C}55∘C

[4]
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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