1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
n200080 [17]
3 years ago
14

A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t

he bacteria is growing at a rate of 4 grams per hour after 3 hours.
Write down the differential equation the mass of the bacteria, m, satisfies: ′= .2m
Find the general solution of this equation. Use A as a constant of integration.
() = Ae^(.2t)
Which particular solution matches the additional information? () =
What was the mass of the bacteria at time =0? mass =
Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
3 0

Answer:

  • <u>Question 1:</u>      dm/dt=0.2m<u />

<u />

  • <u>Question 2:</u>     m=Ae^{(0.2t)}<u />

<u />

  • <u>Question 3:</u>      m=10e^{(0.2t)}<u />

<u />

  • <u>Question 4:</u>      m=10g<u />

Explanation:

<u>Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m</u>

<u></u>

a) By definition:  m'=dm/dt

b)  Given:  rate=0.2m

c) By substitution:  dm/dt=0.2m

<u>Question 2: Find the general solution of this equation. Use A as a constant of integration.</u>

a) <u>Separate variables</u>

     dm/m=0.2dt

b)<u> Integrate</u>

           \int dm/m=\int 0.2dt

            ln(m)=0.2t+C

c) <u>Antilogarithm</u>

       m=e^{0.2t+C}

       m=e^{0.2t}\cdot e^C

         e^C=A\\\\m=Ae^{(0.2t)}

<u>Question 3. Which particular solution matches the additional information?</u>

<u></u>

Use the measured rate of 4 grams per hour after 3 hours

            t=3hours,dm/dt=4g/h

First, find the mass at t = 3 hours

            dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g

Now substitute in the general solution of the differential equation, to find A:

          m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976

Round A to 1 significant figure:

  • A = 10.

<u>Particular solution:</u>

           

             m=10e^{(0.2t)}

<u>Question 4. What was the mass of the bacteria at time =0?</u>

Substitute t = 0 in the equation of the particular solution:

         m=10e^{0}\\\\m=10g

You might be interested in
#5 Antonio and Abby had the same nimber of paperclips. After Antonio gave 30 paperclips to Abby, Abby had twice as many papercli
Kay [80]

Answer:

#5: 180 paperclips in total.

#6: 126 stamps in total.

#7: Elena should give Lucy 15 colored pencils.

Step-by-step explanation:

This explanation solves each question by setting a single unknown, x.

<h3>#5</h3>

Let x the initial number of paperclips of Antonio. That should also be the number of Abby's paperclips.

Initially:

  • Antonio: x paperclips;
  • Abby: x paperclips.

Antonio gives 30 paperclips to Abby. After that,

  • Antonio: (x - 30) paperclips;
  • Abby: x + 30 paperclips.

Abby now possess twice as many paperclips as Antonio does. In other words,

2(x - 30) = x + 30.

By the distributive property:

2x - 60 = x + 30.

Substract x - 60 from both sides

x = 30 - (-60) = 90.

Both Antonio and Abby initially possess 90 paperclips. That's 180 in total.

<h3>#6</h3>

Similarly, let x be the number of Emily's stamps. That should be the same as the number of Jasmine's stamps.

Initially:

  • Emily: x stamps;
  • Jasmine: x stamps.

After Emily gives 42 stamps to Jasmine:

  • Emily: x-42 stamps;
  • Jasmine: x+42 stamps.

Jasmine now possesses twice as many stamps as Emily does. In other words,

2(x-42) = x+42.

x = 42 + 2\times 42 = 126.

Jasmine used to possess 126 stamps. Now she possesses 126 + 42 = 168 stamps after receiving 42 stamps from Emily.

<h3>#7</h3>

Let the number of pencils that Elena needs to give to Lucy be x.

Initially:

  • Elena: 60 pencils;
  • Lucy: 26 pencils.

After Elena gives x pencils to Lucy:

  • Elena: 60 - x pencils;
  • Lucy: 26 + x pencils.

Elena should now possess four more pencils than Lucy does. In other words,

\underbrace{60 - x}_{\text{Elena's}} = \underbrace{(26 + x)}_{\text{Lucy's}} +4.

2x = 30.

x = 15.

8 0
2 years ago
Warm-Up: Solve each equation for x.<br> 1. x + 5 = 15
eduard
X+5=15
-5 -5
X=10
Hope this helps!!
5 0
2 years ago
Read 2 more answers
What is the answer to 5-1/3n=-2
Free_Kalibri [48]

Answer:

21 = n

Step-by-step explanation:

5 - \frac{1}{3}n = -2

-5 - 5

________________

-⅓<em>n</em> = -7

____ __

-⅓ -⅓

21 = <em>n</em>

* Dividing by a fraction is the exact same as multiplying by its <em>multiplicative</em><em> </em><em>inverse</em>:

\frac{-7}{-\frac{1}{3}} = -7 \times -3 = 21

I am joyous to assist you anytime.

4 0
3 years ago
Evaluate 13+6/y when y = 6
uysha [10]
13 + 6/6
13 + 1
14

The answer is 14.

Hope this helps!
8 0
3 years ago
Read 2 more answers
The length of the rectangle is x cm. The length of a diagonal of the rectangle is 8 crn. The perimeter of the rectangle is 20 cm
klemol [59]

Answer:

x^2-10x+18=0

<em>a</em> = -10 and <em>b</em> = 18.

Step-by-step explanation:

Let <em>w</em> represent the width of the rectangle.

We are given that the perimeter of the rectangle is 20 cm, this means that:

20=2(x + w)

Let's put <em>w</em> in terms of <em>x</em>. Divide both sides by two:

10=x+w

And solve for <em>w:</em>

<em />w=10-x<em />

So, the rectangle measures <em>x</em> by (10 -<em> x</em>) cm.

<em />

According to the Pythagorean Theorem:

a^2+b^2=c^2

<em>a</em> and <em>b</em> are the legs and <em>c</em> is the hypotenuse.

Substitute <em>x</em> for <em>a, w</em> for <em>b</em>, and 8 for <em>c:</em>

<em />x^2+w^2=8^2<em />

Simplify and substitute:

x^2+(10-x)^2=64

Square:

x^2+(100-20x+x^2)=64

Isolate the equation. So:

2x^2-20x+36=0

Since the leading coefficient is one, divide both sides by two:

x^2-10x+18=0

Therefore, <em>a</em> = -10 and <em>b</em> = 18.

6 0
2 years ago
Other questions:
  • Ms. Chang has 16 students in her class. She wants to send 3 of her students to pick up books for the class. How many combination
    6·2 answers
  • An assistant is in charge of ordering lunch for the monthly office meeting. For the first month, she orders five Falafel wraps,
    12·2 answers
  • Please help asap !!
    13·1 answer
  • What is the value of x in the equation 3/4(1/4x+8)-(1/2x+2)=3/8(4-x)-1/4x
    5·1 answer
  • PLEASE HELP MEE
    14·2 answers
  • The attendance at a community block party was 3 children for every 2 adults. Which could be the number of children and adults at
    14·1 answer
  • Nswer the following question the best you can.
    8·1 answer
  • Can someone help with these!
    11·1 answer
  • Which one is correct<br> a<br> b<br> c<br> d
    15·2 answers
  • 12. Ben says
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!