By R. M. Haynes, J. G. Harvey, T. D. Davies (auth.), Robin Haynes (eds.)
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21 The height of a stream as a function of distance downstream. Exponential functions are a particular type of logarithmic function. Suppose that you have the sum of £ 100 to invest and that you are able to do so at an interest rate of 10 per cent per annum and that you let the interest be added to the initial investment. The value of your investment I will subsequently be a function of time t: 1= f(t) What will be the value of I when t = 10 years? If the interest were added atthe end of the ten year period, and was calculated as 10 per cent per year of the initial sum invested, the total interest would be 10 x £ 10 = £ 100 and the investment would have become worth £ 200.
The function has the form: i = A +Bt- 1 / 2 which is shown graphically in Fig. 17. 17 The infiltration rate of water into soil with time. Mathematics 41 Power functions are often plotted on double logarithmic graph paper (both axes are logged) which turns the curves into straight lines. 16 are an shown on Fig. 18 with their axes in logarithms. 18 Power functions plotted in logarithmic coordinates. -1 For convenience logarithmic graph paper is printed with logarithmically spaced divisions. L You can achieve the same result by plotting the logarithm of the values of x and y on ordinary linear graph paper.
1 Vector addition Commonly encountered vectors are displacement and velocity. We might state that the distance from Milan to Paris is approximately 640 km but this would not enable a pilot setting off from Milan in an aircraft to find his way to Paris. The information which he would need for this would be the vector quantity displacement, that is, Paris is approximately 640 km from Milan on a bearing 310° (see Fig. 1). Par is x Norr h 11. 1 The displacement of Paris from Milan. Similarly, if we only know the speed of an aircraft we cannot state where it will be at a given time, but if we know that it is leaving Milan at 0900 hand flying towards 310° at a speed of 960 km h - 1, we can state that at 0940 h it will be over Paris.