Decay problem

Algebra Level 3

A substance decays at the rate of 1% per year. How much will it decay in 12 years and six months?

11.9% 12.5% 12.3% 11.8%

Archit Boobna by Archit Boobna , 20, India

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2 solutions

Rajdeep Dhingra
Sep 19, 2014

T h i s i s j u s t a s c o m p o u n d i n t e r e s t w e j u s t n e e d t o a p p l y f o r m u l a o f c o m p o u n d i n t e r e s t b u t d e c r e a s i n g . a m o u n t l e f t i n n y e a r s = 100 ( 1 − 1 100 ) n . s o a m o u n t c o n s u m e d i n 12.5 y e a r s i s 100 ( 1 − ( 1 − 1 100 ) 12.5 = 11.80.......... This\quad is\quad just\quad as\quad compound\quad interest\quad we\quad just\quad need\quad to\quad apply\quad formula\quad of\quad compound\quad interest\quad but\quad decreasing.\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad amount\quad left\quad in\quad n\quad years\quad =\quad 100{ (1-\frac { 1 }{ 100 } ) }^{ n }\quad \quad .\\ so\quad amount\quad consumed\quad in\quad 12.5\quad years\quad is\quad 100(1-{ (1-\frac { 1 }{ 100 } ) }^{ 12.5 }\quad \quad \quad \quad =\quad 11.80..........\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks for the solution!

Archit Boobna - 6 years, 8 months ago
Ramiel To-ong
Jan 6, 2016

NICE SOLUTION

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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