# Homework Help: Changing the water levels of a lake

1. Nov 9, 2015

### Kingyou123

1. The problem statement, all variables and given/known data
Attached problem

2. Relevant equations
Anti-derivatives, linear approx. F(a)=f(a)+F'(a)(x-a)

3. The attempt at a solution
I'm stuck on the first part, I think (w')^-1(1)= W which is 1. It seems too easy... and for part c I'm having trouble finding the equation for the line. I figured that if I graph it on my calculator and use a regression test to find the equation

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Last edited: Nov 9, 2015
2. Nov 9, 2015

### Staff: Mentor

The attachment is way too zoomed out for me to read. Can you type the problem statement into the forum? That would help...

3. Nov 9, 2015

### Kingyou123

updated it, sorry for that.

4. Nov 10, 2015

### HallsofIvy

Is your question just the part that is checked: "(b) Explain what item iv means in terms of the city, lake, and IES budget"?

Item iv is "$(w^{-1})'(1)$". Since w(t) is the depth of water in the lake at time t, $w^{-1}(x)$ is the time at which the level of the lake is x. Then $(w^{-1})'(x)$ is the rate at which time for the water to decrease amount x is changing.

5. Nov 10, 2015

### Kingyou123

My question is on part a, I'm confused what(w')^-1(1) is. Thank you for help with part B :)

Last edited: Nov 10, 2015