Question

The table shows the predicted growth of a particular bacteria after various members of hours. Write an explict formula for the sequence of the number of bacteria.

Answer 1

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:

`\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}`

Now we find the slope m with this formula:

`m=(y_2-y_1)/(x_2-x_1)=(38-19)/(2-1)=(19)/(1)=19;\text{ m=19}`

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:

`(y-y_1)=m(x-x_1)`

We replace the known values and we get:

`(y-19)=19(x-1)`

we solve for y :

`\begin{gathered} (y-19)=19(x-1) \\ y-19=19x-19 \\ y=19x-19+19 \\ y=19x \end{gathered}`

Finally, the formula that describes the secuence of the number of bacteria is

`y=19x`

To comprobate, you can assign diferent numbers of hours to x value and get the number of bacteria corresponding.