Question

The water height of a pool is determined by 5g2 + 3g − 2, the rate that the pool is filled, and 6g2 − 4g − 3, the rate that water leaves the pool, where g represents the number of gallons entering or leaving the pool per minute. Enter an expression that determines the height of the water in the pool. Drag and drop the correct numbers into the boxes to give the water height of the pool if g = 1, 2, 3, and 4.

Answer 1

`h_g=-g^2+7g+1\\\\h_1=7\\\\h_2=11\\\\h_3=13\\\\h_4=13`

Explanation:

Given the rate of filling is
`5g^2+3g-2` and the rate of emptying the pool is
`6g^2-4g-3`. The height of the pool at any time is:

`h_t=R_(in)-R_(out), h_t- \ height \ at\ time\ t\\\\h_t=(5g^2+3g-2)-(6g^2-4g-3)\\\\h_t=-g^2+7g+1`

#Substitute the value of g in the height equation to find the height of the pool:

#g=1

`h_t=-g^2+7g+1, \ g=1\\\\h_t=-(1)^2+7(1)+1\\\\=7`

#g=2

`h_t=-g^2+7g+1, \ g=1\\\\h_t=-(2)^2+7(2)+1\\\\=11`

#g=3

`h_t=-g^2+7g+1, \ g=1\\\\h_t=-(3)^2+7(3)+1\\\\=13`

#g=4

`h_t=-g^2+7g+1, \ g=1\\\\h_t=-(4)^2+7(4)+1\\\\=13`