11th sum plz

Asked by lovemaan5500 | 20th Aug, 2019, 05:12: PM

Expert Answer:

According to the question,
begin mathsize 16px style dx over dt straight alpha space minus straight x
fraction numerator begin display style dx end style over denominator begin display style dt end style end fraction equals negative kx
Integrationg space on space both space sides space we space get
straight x equals straight x subscript 0 straight e to the power of negative kt end exponent
when space straight t equals 25 space years space then space straight x equals left parenthesis 100 percent sign space minus space 1.1 percent sign right parenthesis straight x subscript 0 equals 0.989 straight x subscript 0
0.989 straight x subscript 0 equals straight x subscript 0 straight e to the power of negative 25 straight k end exponent
straight e to the power of negative straight k end exponent equals 0.989 to the power of 1 over 25 end exponent
straight x equals 0.989 to the power of straight t over 25 end exponent straight x subscript 0
when space straight x equals 0.5 straight x subscript 0
0.5 straight x subscript 0 equals 0.989 to the power of fraction numerator begin display style straight t end style over denominator begin display style 25 end style end fraction end exponent straight x subscript 0
0.5 to the power of 25 equals 0.989 to the power of straight t
straight t equals fraction numerator 25 ln 0.5 over denominator ln begin display style 0 end style begin display style. end style begin display style 989 end style end fraction equals 1566.65 space years space end style

Answered by Sneha shidid | 21st Aug, 2019, 10:04: AM