Các hành vi tỷ lệ cố định như là một sửa đổi lần số mũ trong phương trình y = ekt (ví dụ như trong một tài khoản tiết kiệm, k sẽ là lãi suất, như k tăng, nhiều tiền hơn là kiếm được trong cùng thời kỳ của thời gian và đường cong hàm mũ là dốc hơn). Đồ họa đại diện của k (y = ekt) | 12 Section 1 Mathematical principles Rate constant The reciprocal of the time constant. Given the symbol k. or A marker of the rate of change of an exponential process. The rate constant acts as a modifier to the exponent as in the equation y ekt . in a savings account k would be the interest rate as k increases more money is earned in the same period of time and the exponential curve is steeper . Graphical representation of k y ekt k 1 Draw a standard exponential tear-away curve. To move from y et to y et 1 takes time t1. k 2 This curve should be twice as steep as the first as k acts as a 2x multiplier to the exponent t . As k has doubled for the same change in y the time taken has halved and this can be shown as t2 where t2 is half the value of t1. The values t1 and t2 are also the time constants for the equation because they are by definition the reciprocal of the rate constant. Transforming to a straight line graph Start with the general equation as follows y ekt take natural logarithms of both sides ln y ln ekf power functions become multipliers when taking logs giving ln y kt. ln e the natural log of e is 1 giving ln y or ln y kt Exponential relationships and logarithms 13 You maybe expected to perform this simple transformation or at least to describe the maths behind it as it demonstrates how logarithmic transformation can make the interpretation of exponential curves much easier by allowing them to be plotted as straight lines ln y kt. k 1 Draw a curve passing through the origin and rising as a straight line at approximately 45 . k 2 Draw a curve passing through the origin and rising twice as steeply as the k 1 line. The time constant is half that for the k 1 line. Physical measurement and calibration This topic tests your understanding of the ways in which a measurement device may not accurately reflect the actual physiological situation. Accuracy The ability of a measurement device to match the actual value of the quantity being measured. .
