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

Answer:

B. $y=0.75x+1$

Step-by-step explanation:

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

The rate of increase in level of water, $\dfrac{dy}{dt}=0.75\ inch/min.$

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.

Answer 2

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