EXAMPLES XXV 



461 



(9) The following values of x and y were observed in a laboratory 

 and theory suggested that there might be a law y = ax* -f b x 10*. 

 11 K re are errors of observation. Try if there is such a law, and 

 if so, find the probable values of a and b. (B. of E., 1913.) 



(10) The curve y = a -f- bx n passes through the three points 

 (2, 11-5), (4, 18-8), and (8, 39-7) ; find the values of the constants 

 a, b, and n. 



Find the value of y when x = 5. 



(11) The curve y=a+be w passes through the three points 

 (1, 6-8), (3, 13-1), and (5, 25-7) ; find the values of the constants 

 a, b, and n. Find the value of y when x = 4. 



(12) The curve y = a -f be* passes through the three points 

 (2, 5-3), (4, 12-8), and (6, 30-2) ; find the values of the constants 

 a, b, and c. Find the value of y when x = 3. 



(13) The curve y = b (x+ a) n passes through the three points 

 (1 , 29-30) , (3, 40-47) , and (5, 52-28) ; find the values of the constants 

 a, b, and n. Find the value of y when x = 2. 



(14) The following values of x and y might follow the law 

 y = ax + bx Iog 10 x. Try if this is so, and if so, find the most 

 probable values of the constants a and b. (B. of E., 1914.) 



(15) The following values of x and y are thought to follow the 

 law y = a.i bx . Try if this is so, and if so, find the most probable 

 values of the constants a and b. 



(16) Find which of the three laws y = a+ bx n , y = b (x + a) n , 

 and y = a + be"* suit the following values of x and y. 



Having decided upon the probable law, take three points on 

 the curve and find the values of the constants a, b, and n. 



