We have to find a linear equation (yellow line in the graphic) or in the same way, an equation of a line using two ponts of that table.
We are gonna put the number of hous in X axe and the number of bacteria in Y axe, right?
like this:
Now, we gonna place two points, we gona choose the first and the second point..
We aproximate the value in the Y axe, because is to high to place un the graphic..
Then, we have two points, the point A with coordinates (1,19)
and the point B with coordinates (2,38)
Matematically we can write:
[tex]\begin{gathered} (x_1,y_1)=(1,19);x_{1_{}}=1;y_1=19;_{} \\ (x_2,y_2)=(2,38);x_{2_{}}=2;y_2=38; \end{gathered}[/tex]
Now we find the slope m with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{38-19}{2-1}=\frac{19}{1}=19;\text{ m=19}[/tex]
Finally, with the value of the slope and choose one point of the table we're gonna find the general equation of a line, using this formula:
[tex](y-y_1)=m(x-x_1)[/tex]
We replace the known values and we get:
[tex](y-19)=19(x-1)[/tex]
we solve for y :
[tex]\begin{gathered} (y-19)=19(x-1) \\ y-19=19x-19 \\ y=19x-19+19 \\ y=19x \end{gathered}[/tex]
Finally, the formula that describes the secuence of the number of bacteria is
[tex]y=19x[/tex]
To comprobate, you can assign diferent numbers of hours to x value and get the number of bacteria corresponding.
