The value of a car t t\,t years after it was purchased is modelled by the formula V=A+Be−t6\displaystyle V = A + Be^{-\frac{t}{6}}V=A+Be−6t where V V\,V is the value of the car in thousands of pounds, and A A\,A and B B\,B are constants.
The graph of V V\,V against t t\,t passes through (0,18)(0, 18)(0,18) and (6,7)(6, 7)(6,7), and the line V=kV = kV=k is an asymptote to the curve.
Find the values of AAA, B B\,B and kkk, giving your answers to 3 significant figures where appropriate.
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.