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.
62 exam-style questions on AQA A Level Maths 1.9 F: Exponentials and logarithms, covering 1.9.1 Exponential functions and their graphs, 1.9.2 Gradient of e^kx (A-level only), 1.9.3 Logarithms as inverse functions, 1.9.4 Laws of logarithms, 1.9.5 Solving exponential equations, 1.9.6 Logarithmic graphs to estimate parameters (A-level only), and 1.9.7 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.