Question

An oil tank is being filled at a constant rate the depth of the oil is a function of the number of minutes has been filling, as shown in the table find the depth of the oil 1/2 hour after filling begins
Time:0,10,15
Depth:3,5,6
(0,3) (10,5) (15,6)

Answer 1

We are given time in minutes.

According to given table, we are given times 0 minute, 10 minutes and 15 minutes.

And depths are given 3, 5 and 6.

Times represents x coordinates and depths represents y-coordinates.

First we need to find the depth of the tank in per unit time( in a minute).

In order to find the depth of the tank in per unit time, we need to find th slope between two coordinates.

Let us take first two coordinate made using table (0,3) (10,5)

We know, slope formula

$m=\frac{y_2-y_1}{x_2-x_1}$

Plugging values in slope formula, we get

m= $\frac{5-3}{10-0}=\frac{2}{10}=\frac{1}{5}$

We got slope m= 1/5=0.2.

We can say that depth of the tank is increasing by rate 0.2 per minute.

From the given table, we can see that for x=0, y value is 3.

Therefore, y-intercept is 3.

Let us write an equation of the line for given table in slope-intercept form y=mx+b.

Plugging values of m and b in slope-intercept form, we get

y= 0.2x+3.

We need to find the depth after 1/2 hours.

1 hour = 60 minutes,

Therefore, 1/2 hours = 60/2 = 30 minutes.

Plugging value of x=30 in above slope-intercept form of the equation, we get

y= 0.2(30)+3.

y= 3+6 = 9.

y=9

Therefore, the depth of the oil 1/2 hour after filling begins is 9 units.