Michael's car is valued after 2 years and after 5 years. V=Ae−ktV = Ae^{-kt}V=Ae−kt.
| Time (years) | 2 | 5 |
|---|---|---|
| Value (£) | 47200 | 29200 |
Explain what the value of A A\,A represents.
Show that lnV=lnA−kt\ln V = \ln A - ktlnV=lnA−kt
Calculate the value of A A\,A and the value of kkk
Use the model to predict the value of the car after 10 years.
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.