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 (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.