Home
Class 12
BIOLOGY
What does 'e' represent in the integral ...

What does 'e' represent in the integral form of exponential growth equation given below?
`N_(t)=N_(0)e^(rt)`

A

Population density at time 't'

B

Population density at time 0

C

Intrinsic rate of natural increase

D

The base of natural logarithm

Text Solution

AI Generated Solution

The correct Answer is:
To answer the question about what 'e' represents in the integral form of the exponential growth equation \( N_t = N_0 e^{rt} \), we can break down the components of the equation step by step. ### Step-by-Step Solution: 1. **Understanding the Equation**: The equation \( N_t = N_0 e^{rt} \) describes how a population grows over time under ideal conditions. Here, \( N_t \) is the population size at time \( t \), \( N_0 \) is the initial population size, \( r \) is the intrinsic rate of natural increase, and \( t \) is the time. 2. **Identifying 'e'**: In this equation, 'e' is a constant that is approximately equal to 2.71828. It is known as the base of the natural logarithm. 3. **Role of 'e' in Exponential Growth**: The presence of 'e' in the equation indicates that the growth of the population is exponential. This means that as time increases, the population grows at a rate proportional to its current size, leading to rapid increases. 4. **Conclusion**: Therefore, 'e' represents the base of natural logarithms, which is crucial for describing continuous growth processes in mathematics and biology. ### Final Answer: In the integral form of the exponential growth equation \( N_t = N_0 e^{rt} \), 'e' represents the base of natural logarithms.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ORGANISMS AND POPULATIONS

    AAKASH SERIES|Exercise EXERCISE-I (LIFE HISTORY VARIATION)|3 Videos

  • ORGANISMS AND POPULATIONS

    AAKASH SERIES|Exercise EXERCISE-I (POPULATION INTERACTIONS)|46 Videos

  • ORGANISMS AND POPULATIONS

    AAKASH SERIES|Exercise EXERCISE-I (ADAPTATIONS)|12 Videos

  • NEURAL CONTROL AND COORDINATION

    AAKASH SERIES|Exercise EXERCISE-III( PREVIOUS AIPMT / NEET QUESTIONS)|33 Videos

  • PHOTOSYNTHESIS IN HIGHER PLANTS

    AAKASH SERIES|Exercise Exercise - III|27 Videos

Similar Questions

Explore conceptually related problems

The integral form of exponential growth equation will be

What does 'K' represent in the equation given below? (dN)/(dt)=rN((K-N)/(K))

In the equation N_(t)=N_(0)e^(rt),'e' is

In exponential growth formula, W_(t)=W_(0)e^(rt),e denotes

L_(1)=L_(0)+rt . What does L(0) represent in the given expression?

The integrating factor of the differential equation (dy)/(dx)(x(log)_e x)+y=2(log)_e x is given by

The integrating factor of the differential equation (dy)/(dx)(x(log)_e x)+y=2(log)_e x is given by

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. y=a e^(3x)+b e^(-2x)

The rate of reaction increases isgnificantly with increase in temperature. Generally, rate of reactions are doubled for every 10^(@)C rise in temperature. Temperature coefficient gives us an idea about the change in the rate of a reaction for every 10^(@)C change in temperature. "Temperature coefficient" (mu) = ("Rate constant of" (T + 10)^(@)C)/("Rate constant at" T^(@)C) Arrhenius gave an equation which describes aret constant k as a function of temperature k = Ae^(-E_(a)//RT) where k is the rate constant, A is the frequency factor or pre-exponential factor, E_(a) is the activation energy, T is the temperature in kelvin, R is the universal gas constant. Equation when expressed in logarithmic form becomes log k = log A - (E_(a))/(2.303 RT) Activation energies of two reaction are E_(a) and E_(a)' with E_(a) gt E'_(a) . If the temperature of the reacting systems is increased form T_(1) to T_(2) ( k' is rate constant at higher temperature).

Let E,G and N represent the magnitudes of electromagnetic, gravitational and nuclear forces between two electrons at a given separation. Then

Home
Profile