CBSE Class 11-science Answered

WHILE WRITING LOG a WITH BASE e, HOW DID THE VALUE OF e CAME?

Asked by ramkishoreagrawal50 | 07 Dec, 2015, 06:46: PM

Expert Answer

$apostrophe e apostrophe space i s space c a l l e d space t h e space e u l e r apostrophe s space c o n s tan t comma space w h i c h space i s space t h e space b a s e space o f space t h e space n a t u r a l space log a r i t h m. I t space i s space a p p r o x i m a t e l y space e q u a l space t o space 2.71828... T h e space v a l u e space o f space e space c a n space b e space d e r i v e d space f r o m space t h e space t h e o r y space o f space c o m p o u n d space i n t e r e s t. L e t space u s space s t a r t space a n space a c c o u n t space w i t h space R e.1 S u p p o s e space t h e space b a n k space i s space p a y i n g space 100 percent sign c o m p o u n d space i n t e r e s t space p e r space y e a r. T h e r e f o r e comma space t h e space a m o u n t space o f space m o n e y space c r e d i t e d space t o space y o u r space a c c o u n t space a f t e r space o n e space y e a r space w i l l space b e space R s.2. A s s u m i n g space t h e space b a n k space i s space p r o v i d i n g space 100 percent sign space h a l f space y e a r l y comma space t h e r e f o r e comma A m o u n t equals 1 open parentheses 1 plus 100 over 200 close parentheses squared equals 1.5 squared equals R s.2.25 A s s u m i n g space t h e space b a n k space i s space p r o v i d i n g space 100 percent sign space q u a r t e r l y comma space w e space h a v e comma A m o u n t equals 1 open parentheses 1 plus 100 over 400 close parentheses to the power of 4 equals 1.25 to the power of 4 equals R s.2.4414... . . . . A s s u m i n g space t h e space b a n k space i s space p r o v i d i n g space 100 percent sign space m o n t h l y comma space w e space h a v e comma A m o u n t equals 1 open parentheses 1 plus 100 over 1200 close parentheses to the power of 12 equals 1.25 to the power of 4 equals R s.2.692597... .... B y space f i n d i n g space t h e space c o m p o u n d space i n t e r e s t space o f space R e.1 space f o r space 100 percent sign space r a t e comma space a t space n space c o m p o u n d i n g space i n t e r v a l s space y i l e d s space t o R s.1 cross times open parentheses 1 plus 1 over n close parentheses to the power of n W h e n space apostrophe n apostrophe space i n c r e a s e s space t o space i n f i n i t y comma space t h e space a m o u n t space y i e l d s space t o space 2.71828... T h i s space i s space a space c o n s tan t.$