Maths-
General
Easy

Question


Which equation is the most appropriate exponential model for the data shown in the scatterplot?

  1. y equals 1 over 100 left parenthesis 10 right parenthesis to the power of x
  2. y equals 2 left parenthesis 5 right parenthesis to the power of x
  3. y equals 6 left parenthesis 2 right parenthesis to the power of x
  4. y equals 100 left parenthesis 2 right parenthesis to the power of negative x end exponent

The correct answer is: y equals 6 left parenthesis 2 right parenthesis to the power of x


    HINT :- Check the appropriate equation at point 1 ,2 ,3 and 4.
    Explanation : By option checking at points 1,2,3,4
    Step:-1 checking option a
    y space equals space 1 over 100 space left parenthesis 10 right parenthesis to the power of x at x= 0 rightwards double arrow y = 0.01( lies between 0 to 20 as shown in graph)
    at x= 1 rightwards double arrow y = 0.1( lies between 0 to 20 as shown in graph)
    at x= 2 rightwards double arrow y = 1( does not lies between 20 to 40 as shown in graph)
    SO, not option A.
    Step 2:checking option B
    y space equals space 2 space left parenthesis 5 right parenthesis to the power of x at x= 0 rightwards double arrow y = 2( lies between 0 to 20 as shown in graph)
    at x= 1rightwards double arrow y = 10( lies between 0 to 20 as shown in graph)
    at x= 2 rightwards double arrow y = 50( does not lies between 20 to 40 as shown in graph)
    SO, not option B.
    Step 3:checking option c
    y space equals space 6 left parenthesis 2 right parenthesis to the power of x at x= 0 rightwards double arrow y = 6( lies between 0 to 20 as shown in graph)
    at x= 1 rightwards double arrowy = 12( lies between 0 to 20 as shown in graph)
    at x= 2 rightwards double arrowy = 24(  lies between 20 to 40 as shown in graph)
    at x= 3 rightwards double arrowy = 48(  lies between 40 to 60 as shown in graph)
    at x= 4 rightwards double arrow y = 96(  approximately = 100 as shown in graph)
    SO, option Cis the correct representation of data shown in scatter plot.

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