Mathbee · CBSE Class 12 Maths

NCERT Class 12 · Ch 9 Exercise 9.3 · Q22

NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 22

A culture starts with 100000 bacteria and grows by 10% in 2 h, at a rate proportional to population. When does it reach 200000?

Exponential culture growth (population in units of 100000)

💡 Concept Hints

Identify the domain and the inner and outer functions, or the relevant one-sided limits.
Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.

✅ Step-by-Step Solution

Final Answer: t=2log 2/log(1.1)≈14.545 hours from the initial time.

N′=kN gives N=100000e^(kt). The two-hour observation gives e^(2k)=1.1, so k=log(1.1)/2.
For doubling, e^(kt)=2; therefore t=log 2/k=2log 2/log(1.1).

Master Chapter 9: Differential Equations

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Differential Equations.

📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →

← Previous Question

₹1000 grows continuously at 5%/year. Find its value after 10 years…

Next Question →

Choose the general solution of y′=e^(x+y).

All Questions in Differential Equations — Exercise 9.3

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23

Related Questions in Differential Equations

Class 12 Differential Equations · Mcq Single Correct

Find the degree of x²y″ = (xy′ − y)³.

Class 12 Differential Equations · Mcq Single Correct

Find the degree of y″ + 3(y′)² = x² ln(y″).

Class 12 Differential Equations · Mcq Single Correct

Find the order and degree of [1 + (y′)²]² = y″.

Class 12 Differential Equations · Mcq Single Correct

The nonconstant solutions of 2xy′ − y = 3 lie on a family of which curves?

Class 12 Differential Equations · Mcq Single Correct

Find an integrating factor of (x ln x)y′ + y = 2 ln x, for x > 0, x ≠ 1.

Class 12 Differential Equations · Mcq Single Correct

Which function satisfies (y′)² − xy′ + y = 0?