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Maths-

General

Easy

Question

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

$y = \frac{1}{100} (10)^{x}$
$y = 2 (5)^{x}$
$y = 6 (2)^{x}$
$y = 100 (2)^{- x}$

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= 1 $rightwards double arrow$ 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 $rightwards double arrow$ y = 12( lies between 0 to 20 as shown in graph)
at x= 2 $rightwards double arrow$ y = 24( lies between 20 to 40 as shown in graph)
at x= 3 $rightwards double arrow$ y = 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.

Related Questions to study

$S left parenthesis t right parenthesis equals 10 left parenthesis 0.5 right parenthesis to the power of t over 29 end exponent$
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