Home
Class 12
PHYSICS
Which of the following graph is the best...

Which of the following graph is the best presentation for the given equation `y=2e^(x)`

A

B

C

D

Text Solution

AI Generated Solution

The correct Answer is:
To determine which graph best represents the equation \( y = 2e^x \), we can follow these steps: ### Step 1: Understand the Equation The given equation is \( y = 2e^x \). This is an exponential function where \( e \) (approximately 2.71) is the base of the natural logarithm. ### Step 2: Calculate Key Points We can calculate the value of \( y \) for some specific values of \( x \): - For \( x = 0 \): \[ y = 2e^0 = 2 \times 1 = 2 \] - For \( x = 1 \): \[ y = 2e^1 = 2 \times 2.71 \approx 5.42 \] - For \( x = 2 \): \[ y = 2e^2 = 2 \times (2.71^2) \approx 2 \times 7.39 \approx 14.78 \] - For \( x = 3 \): \[ y = 2e^3 = 2 \times (2.71^3) \approx 2 \times 20.08 \approx 40.16 \] ### Step 3: Analyze the Graphs Now, we need to analyze the graphs provided (let's assume they are labeled A, B, C, and D): 1. **Check the point at \( x = 0 \)**: The graph should pass through the point (0, 2). 2. **Check the growth of \( y \)**: As \( x \) increases, \( y \) should also increase rapidly since it is an exponential function. ### Step 4: Compare Graphs - **Graph A**: At \( x = 0 \), \( y = 1 \) (incorrect). - **Graph B**: At \( x = 0 \), \( y = 2 \) (correct) and appears to be increasing. - **Graph C**: At \( x = 0 \), \( y = 1 \) (incorrect). - **Graph D**: At \( x = 0 \), \( y = 2 \) (correct) but appears to be decreasing. ### Step 5: Conclusion Based on the analysis: - Graph B is the best representation of the equation \( y = 2e^x \) because it correctly shows the point (0, 2) and the increasing nature of the function. ### Final Answer The best presentation for the equation \( y = 2e^x \) is **Graph B**.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RACE

    ALLEN|Exercise Basic Maths (Co-ordinate & Algebra)|37 Videos
  • RACE

    ALLEN|Exercise Basic Maths (VECTORS)|60 Videos
  • RACE

    ALLEN|Exercise Basic Maths (Integration)|12 Videos
  • NEWTONS LAWS OF MOTION

    ALLEN|Exercise EXERCISE-III|28 Videos
  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Example|1 Videos

Similar Questions

Explore conceptually related problems

Which of the following is the best representation of the following graph ?

Which of the following equation is best representation of given graph's?

Knowledge Check

  • In a experiment a set of points denoted by the (x,y) coordinates are shown in the graph above along with the line of best fit. Which of the following is the best equation for the above line ?

    A
    y = 0.7x - 3.7
    B
    y = 0.9x + 15.8
    C
    y =1.2x - 6.8
    D
    y = 1.2x + 12.3
  • Similar Questions

    Explore conceptually related problems

    Which of the following equation is best representation of given graph's?

    Which of the following equation is best representation of given graph's?

    Which of the following equation is best representation of given graph's?

    Which of the following equation is best representation of given graph's?

    Which of the following equation is best representation of given graph's?

    Draw the Graph for the given equation. - (i) y=2x

    Which of the following graphs best represents the variation of acceleration 'a' with displacement x?