Growth in General 15 



ments themselves continually increase. The equation for "compound- 

 interest" growth is the familiar one 



?i = P e rt 



where Pi is the size at any time t; P the size at the beginning of growth; 

 e the base of the natural logarithms, 2.18; and r the rate of growth (in- 

 terest or exponential rate). This can be expressed, by using common 

 logarithms, as 



logP 1 = logP + loge(rt) 



To find r for the first 10 days in Table 2-1, we substitute in this equa- 

 tion as follows: 



1.4771 = 0.3802 + 0.4343 X lOr 



1.4771 - 0.3802 



r = 



= 0.25 



10 X 0.4343 



This is the rate of diameter increase per day at which, continuously com- 

 pounded, this fruit is growing, expressed as a per cent of its previous 

 growth. If the logarithms of the successive size of gourd fruits in Table 2-1 

 are plotted against time (or the data plotted on semilogarithmic paper) 

 the graph in Fig. 2-3 results. Here the growth for the first 10 days is seen 



E 

 E 



O 



Time in days 



Fig. 2-3. Curve of the logarithm of fruit diameter in Table 2-1 plotted against time in 

 days. 



