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.