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Trout, Moose, and Bear lakes are connected into a chain by a stream that runs into Trout Lake, out of Trout Lake into Moose Lake, out of Moose Lake and into Bear Lake and out of Bear Lake. The volumes of all of the three lakes are the same, and stream flow is constant into and out of all lakes. A load of waste is dumped into Trout Lake. With $t$ measured in days and concentration measured in $\mathrm{mg} / \mathrm{l}$, the concentration of wastes in the three lakes is projected to be$$\begin{array}{ll}\text { Trout Lake: } & C_{\mathrm{T}}(t)=0.01 e^{-0.05 t} \\\text { Moose Lake: } & C_{\mathrm{M}}(t)=0.005 t e^{-0.05 t} \\\text { Bear Lake: } & C_{\mathrm{B}}(t)=0.000025 \frac{t^{2}}{2} e^{-0.05 t}\end{array}$$For each lake, find the time interval, it any, on which the concentration in the lake is increasing.

Calculus 1 / AB

Chapter 8

Applications of Derivatives

Section 1

Some geometry of the derivative

Differentiation

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

44:57

In mathematics, a differen…

01:54

03:03

A landlocked lake has been…

01:26

Fish A landlocked lake has…

13:24

The daily discharge of the…

07:09

At Fontaine Lake Camp on L…

29:02

Pollution Pollution begins…

02:54

A fishery stocks a pond wi…

01:48

The Environmental Protecti…

01:33

02:18

Pollution Pollution from a…

01:03

02:25

Fish Food Requirements A l…

05:41

A stream feeds into a lake…

11:07

04:47

The number of bass in a …

01:27

Trout population One thous…

04:57

Pollution A lake polluted …

02:26

Stocking a lake: A farmer …

03:24

Solve each problem.Tro…

01:47

Sediment To develop strate…

07:55

Review. A Chinook salmon c…

in year 2000 and 15. The populace enough throughout, will be given by peanut, and that is equal to 5500. Find that as for the cushion, we know that 500 tarts are stocked in the leg buddy. But every year the number off throat decreases by 75% off the number off I thought last year, but as a whole regiments and that 500 stores are also added, so the sequence will be given a speech in will be equal to 0.75 multiplied by being minus one plus 500. This is recursive sequence. That means to using the previous time they can find out the next times. In be part, we have anything close to one than be one is equals to 0.75 multiplied by 5500 plus 500 that is equal to 4625 for any Balto. P two is given a 0.75 off P one plus 500 that is equal to 3916 for an equal to three. Petri is given a 0.75 multiplied by 396 men plus 500 that is equal to 2477 foreign equal to food. That means in the ear 40 years after 2015 before is given as 3468. As we can object from all the above deter that then the population of thought keeps on decreasing as time passes. For that, we can use the graphing utility. Do I understand the trend off the population of tort? So as you can see in the graph the populace and kept on decreasing after 2010 15. So from graphing utility, we can observe that as time passes, the population off trout decreases. But the rate off decree mint kept on decreasing, so decreases with decreasing there. Why? Because at each year, 75% off the current population of thought, Dimon's but 500 added also

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In mathematics, a differentiation rule is a rule for computing the derivativ…

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