SOLUTION: Bacteria grow in colonies over time. Which table shows growth of bacteria colonies that can be modeled by a linear graph? A.Time (in hours) 1,2,3,4 Number ofcolonies 1,4,9,16

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Question 1153197: Bacteria grow in colonies over time. Which table shows growth of bacteria colonies that can be modeled by a linear graph?
A.Time (in hours) 1,2,3,4
Number ofcolonies 1,4,9,16
B. Time (in hours) 1,2,3,4
Numbers of colonies 5,10,15,20
C.Time (in hours) 1,2,3,4
Numbers of colonies 1,16,81,256
D. Time (in hours) 1,2,3,4
Number of colonies 5,25,125,625
Found 3 solutions by josgarithmetic, MathLover1, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
B. is obviously linear since the data show a constant slope from data pair to data pair. You should be able to find any others. (Looks like none others)
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

growth of bacteria colonies that can be modeled by a linear graph?
first determine if points lie in a line
A.Time (in hours) ,,,
Number of colonies ,,,
Solved by pluggable solver: To determine if 3 points lie in a line
The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.


In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope.


Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.


Slope of line taking points (X1,Y1) and (X2,Y2) is




........................(1)



Slope of line taking points (X3,Y3) and (X1,Y1) is




........................(2)



From conditions (1) and (2)


The 3 points do not a same line.


For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.


Here the slopes are unequal hence the points do not lie on same line.


To read more on equations of a line refer to articles on wikipedia


The points do not a same line.=>not your answer

B. Time (in hours) ,,,
Numbers of colonies ,,,
It is proved that the on line

C.Time (in hours) ,,,
Numbers of colonies ,,,
Solved by pluggable solver: To determine if 3 points lie in a line
The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.


In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope.


Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.


Slope of line taking points (X1,Y1) and (X2,Y2) is




........................(1)



Slope of line taking points (X3,Y3) and (X1,Y1) is




........................(2)



From conditions (1) and (2)


The 3 points do not a same line.


For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.


Here the slopes are unequal hence the points do not lie on same line.


To read more on equations of a line refer to articles on wikipedia


The points do not a same line.=>not your answer
D. Time (in hours) ,,,
Number of colonies ,,,
Solved by pluggable solver: To determine if 3 points lie in a line
The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.


In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope.


Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.


Slope of line taking points (X1,Y1) and (X2,Y2) is




........................(1)



Slope of line taking points (X3,Y3) and (X1,Y1) is




........................(2)



From conditions (1) and (2)


The 3 points do not a same line.


For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.


Here the slopes are unequal hence the points do not lie on same line.


To read more on equations of a line refer to articles on wikipedia


The points do not a same line.=>not your answer

so, answer is B:
let find equation using point-slope formula:

use two points to find a slope





check the graph:


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Bacteria grow in colonies over time. Which table shows growth of bacteria colonies that can be modeled by a linear graph?
A.Time (in hours) 1,2,3,4
Number ofcolonies 1,4,9,16
B. Time (in hours) 1,2,3,4
Numbers of colonies 5,10,15,20
C.Time (in hours) 1,2,3,4
Numbers of colonies 1,16,81,256
D. Time (in hours) 1,2,3,4
Number of colonies 5,25,125,625
For this to be linear, an INCREASE in time must be CONSISTENT (same), and accompanied by a CONSISTENT (same) INCREASE in colonies. 

Now, choose the answer that represents this!!

That's ALL!! Nothing COMPLEX!! 

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