Changing the water levels of a lake

[Kingyou123]

Homework Statement

Attached problem

Homework Equations

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

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

 

[berkeman]

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

 

[Kingyou123]

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

updated it, sorry for that.

 

[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.

 

[Kingyou123]

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.

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