Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.11 question 2

Provide solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.11 question 2

Answers (1)

Answer: 20\log 2 years

Given:  Population growth rate =5% per year.

To find: Time taken for increase in population.

Hint: The rate of population increases with increase in time i.e. \frac{d P}{d t}=r \% \times P

Solution: Population growth rate =5% per year

Let initial population be P_{0}  and the population after time t be P

Then,

        \begin{aligned} &\frac{d P}{d t}=5 \% \times P \\\\ &=\frac{d P}{d t}=\frac{5}{100} \times P \end{aligned}

        =>\frac{d P}{d t}=\frac{P}{20}

By cross multiplication we get,

        =>20 \frac{d P}{p}=d t

Integrating on both sides

        \begin{aligned} &=>20 \int \frac{d P}{P}=\int d t \\\\ &=>20 \log P=t+C \ldots(i) \end{aligned}

At t=0 we have P=P_{0}                                 [Putting t=0 and P=P_{0} in equation i]       

        \begin{aligned} &=>20 \log \left(P_{0}\right)=0+C \\\\ &=>C=20 \log P_{0} \end{aligned}        

Putting C=20 \log P_{0}  in equation (i)

        \begin{aligned} &=>20 \log P=t+20 \log \left(P_{0}\right) \\\\ &=>20 \log P-20 \log \left(P_{0}\right)=t \\\\ &=>20 \log \frac{p}{p_{0}}=t \end{aligned}

When P=2 P_{0} we get

        \begin{aligned} &=20 \log \left(\frac{2 P_{0}}{P_{0}}\right) \\\\ &=t=20 \log 2 \end{aligned}

Hence, the required time period is 20\log 2  years.

 

Posted by

infoexpert26

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question