Question

There is 1 in. of water in a pool. The water level is increasing at 0.75 in./min . Which linear equation represents the total depth of the water, in inches, after x minutes?

A. 1+y=0.75x

B. y=0.75x+1

C. y=0.75x

D. x=0.75y

Answer 1

I think it is B. y=0.75x+1. I think that 1 in. of water in a pool is the y-intercept.

Answer 2

B.
`y=0.75x+1`

Explanation:

Initial level of pool,
`y_i=1 \ inch.`

The rate of increase in level of water,
`(dy)/(dt)=0.75\ inch/min.`

Now, to find relation between depth and time .

From above equation,
`dy=0.75\ dt`.

Now at time = 0 min depth is 1 inch and at any time t=x min and depth=y inch.

Therefore,
`\int\limits^y_1 \, dy=0.75\int\limits^x_0 \, dt`.

Integrating both sides,

We get
`y|_1^y=0.75\ t|_0^x`

`y-1=0.75x`

`y=0.75x+1`

Therefore , correct answer is B.

Hence, it is the required solution.