Solution to 7. Separation of variablesbecome dr ue integral evaluate to: In 3y +2 = + cApply e to get: 3y + 2 ca. Some algebra yields the general solution: yimplies c4 = 26 So the particular solution is: | y 26e3a--dr. Use 1-substitution with u 3y+2 and - dy. The integrals13y + 2l duApply some algebra to get: In 3y +2 = 3x + c22c4e3Use IC to find C4 : 8-y(0)Exponential Growth and Mixing problems homework to be handed in. Just two problems:Problem 1. (Exponential growth) Suppose a small colony of 1,000 bacteria, at t 0 minutes is in a large bottle of waterwith lots of food and no predators (so there are no predation or density dependent issues to worryminutes there are 2,500 bacteria in the colony. Let y(t) = the number oin a largeabout). Suppose after 45f bacteria in the colony at time t, t measured in minutesWrite the ODE IVP for the above scenario and find the solution to the IVP. Use the solution to estimate how many bacteriain the bottle at t90 minutes. Circle your answer (the number of bacteria after 90 minutes).werelem 2. (Mixing) We start with 2,000 liters of seawater in a tank. In seawater there are 35 g of salt per liter. Supposewe continually pour fresh water (0.5 g salt/liter) into the top of the tank at the rate of 10 liters/minute and at the bottom ofthe tank, we continually drain off 10 liters/minute. So the amount of water in the tank is always 2,000 liters. Assume that thewater in the tank is being stirred so that the saltwater and the freshwater mix immediately. How long until the concentofrationsalt in the tank is 6 g/liter? Circle your final answer (how many minutes until the salt concentration is 6 g/L)Instructions. On page 1, immediately after your name, write:(1) Number of bacteria after 90 min = your answer(2) Minutes until the salt concentration is 6 g/LyoThen, underneath and on the following pages show all work. Don't skip steps. Show the integration. Use a pencil (so youcan erase your mistakes). Be neat so that I can follow your work. Circle final answers. STAPLE with stapler the pages. Nopaper clips, etc.

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Asked Feb 14, 2019
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Question 2

Solution to 7. Separation of variables
become dr ue integral evaluate to: In 3y +2 = + c
Apply e to get: 3y + 2 ca. Some algebra yields the general solution: y
implies c4 = 26 So the particular solution is: | y 26e3a-
-dr. Use 1-substitution with u 3y+2 and - dy. The integrals
1
3y + 2
l du
Apply some algebra to get: In 3y +2 = 3x + c2
2
c4e3
Use IC to find C4 : 8-y(0)
Exponential Growth and Mixing problems homework to be handed in. Just two problems:
Problem 1. (Exponential growth) Suppose a small colony of 1,000 bacteria, at t 0 minutes is in a large bottle of water
with lots of food and no predators (so there are no predation or density dependent issues to worry
minutes there are 2,500 bacteria in the colony. Let y(t) = the number o
in a large
about). Suppose after 45
f bacteria in the colony at time t, t measured in minutes
Write the ODE IVP for the above scenario and find the solution to the IVP. Use the solution to estimate how many bacteria
in the bottle at t
90 minutes. Circle your answer (the number of bacteria after 90 minutes).
were
lem 2. (Mixing) We start with 2,000 liters of seawater in a tank. In seawater there are 35 g of salt per liter. Suppose
we continually pour fresh water (0.5 g salt/liter) into the top of the tank at the rate of 10 liters/minute and at the bottom of
the tank, we continually drain off 10 liters/minute. So the amount of water in the tank is always 2,000 liters. Assume that the
water in the tank is being stirred so that the saltwater and the freshwater mix immediately. How long until the concent
of
ration
salt in the tank is 6 g/liter? Circle your final answer (how many minutes until the salt concentration is 6 g/L)
Instructions. On page 1, immediately after your name, write:
(1) Number of bacteria after 90 min = your answer
(2) Minutes until the salt concentration is 6 g/Lyo
Then, underneath and on the following pages show all work. Don't skip steps. Show the integration. Use a pencil (so you
can erase your mistakes). Be neat so that I can follow your work. Circle final answers. STAPLE with stapler the pages. No
paper clips, etc.
help_outline

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Solution to 7. Separation of variables become dr ue integral evaluate to: In 3y +2 = + c Apply e to get: 3y + 2 ca. Some algebra yields the general solution: y implies c4 = 26 So the particular solution is: | y 26e3a- -dr. Use 1-substitution with u 3y+2 and - dy. The integrals 1 3y + 2 l du Apply some algebra to get: In 3y +2 = 3x + c2 2 c4e3 Use IC to find C4 : 8-y(0) Exponential Growth and Mixing problems homework to be handed in. Just two problems: Problem 1. (Exponential growth) Suppose a small colony of 1,000 bacteria, at t 0 minutes is in a large bottle of water with lots of food and no predators (so there are no predation or density dependent issues to worry minutes there are 2,500 bacteria in the colony. Let y(t) = the number o in a large about). Suppose after 45 f bacteria in the colony at time t, t measured in minutes Write the ODE IVP for the above scenario and find the solution to the IVP. Use the solution to estimate how many bacteria in the bottle at t 90 minutes. Circle your answer (the number of bacteria after 90 minutes). were lem 2. (Mixing) We start with 2,000 liters of seawater in a tank. In seawater there are 35 g of salt per liter. Suppose we continually pour fresh water (0.5 g salt/liter) into the top of the tank at the rate of 10 liters/minute and at the bottom of the tank, we continually drain off 10 liters/minute. So the amount of water in the tank is always 2,000 liters. Assume that the water in the tank is being stirred so that the saltwater and the freshwater mix immediately. How long until the concent of ration salt in the tank is 6 g/liter? Circle your final answer (how many minutes until the salt concentration is 6 g/L) Instructions. On page 1, immediately after your name, write: (1) Number of bacteria after 90 min = your answer (2) Minutes until the salt concentration is 6 g/Lyo Then, underneath and on the following pages show all work. Don't skip steps. Show the integration. Use a pencil (so you can erase your mistakes). Be neat so that I can follow your work. Circle final answers. STAPLE with stapler the pages. No paper clips, etc.

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