Question

I dont get none of this please help 30 points

Answer 1

If
`L(d)` is the water level after
`d` days, then at the start
`(d=0)` we have
`L(0)=21`. After the first day
`(d=1)`, the water level falls by 1.5, so that
`L(1)=21-1.5=19.5`. After the second day
`(d=2)`, the water level falls by a total of 2(1.5) = 3, so that
`L(2)=21-2(1.5)=18`. And so on.

The idea is that
`L(d)` has the closed form
`L(d)=21-1.5d` (to answer part b).

`d` could be any non-negative number of days, which means we can pick
`d` from the set of non-negative real numbers. However, after a certain point, our function
`L(d)` will start returning negative values, which would translate to the water level falling below the riverbed. So for the purposes of this problem, we should first find out when
`L(d)` reaches 0:

`L(d)=21-1.5d=0\implies d=14`

That is, the river dries up completely after 14 days. So we can say the domain of
`L(d)` is
`0\le d\le14`.

The range is the set of values that
`L(d)` can take on for the values of
`d` in the domain. In this case, we start at 21 and steadily fall to 0, so the range is
`0\le L(d)\le21`.

After 9 days, the water level falls to

`L(9)=21-9(1.5)=7.5`

so in total, the water level would have subsided by a depth of 21 - 7.5 = 13.5 ft.