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
GrogVix [38]
3 years ago
6

The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 3 hours

it is observed that 500 bacteria are present. After 10 hours 5000 bacteria are present. What was the initial number of bacteria
Mathematics
1 answer:
Arada [10]3 years ago
8 0

Answer:

The number of bacteria at initial = 187

Step-by-step explanation:

Given that the population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t.

\frac{dN}{dt} = k N

\frac{dN}{N}  = k dt

Integrating both side we get

㏑ N = k t + C ------- (1)

Now given that after 3 hours it is observed that 500 bacteria are present and after 10 hours 5000 bacteria are present.

⇒ ㏑ 500 = 3 k + C -------- (2)

⇒ ㏑ 5000 = 10 k + C ------ (3)

⇒ ㏑ 5000 -  ㏑ 500 = 7 k

⇒ ㏑\frac{5000}{500} = 7 k

⇒  ㏑ 10 = 7 k

⇒ k = 0.329

Put this value of k in equation (2),

⇒ ㏑ 500 = 3 × 0.329 + C

⇒ C = 5.23

Put this value of C in equation 1 we get,

⇒ ㏑ N = k t + 5.23

Initially when t = 0 , then

⇒ ㏑ N = 5.23

⇒ N =  187

Thus the number of bacteria at initial = 187

You might be interested in
Please help, I need the answer
Oxana [17]
9189.15 ft (this is the answer and I have not rounded it)
6 0
3 years ago
Read 2 more answers
WILL MARK BRAINLIEST HELP ASAP ASAP
Alina [70]

Answer:

B

Step-by-step explanation:

I got this answer correct on a test

5 0
2 years ago
It costs $100 to rent a bowling alley, plus $4 per person. The cost for any number (n) of people can be found using the expressi
AfilCa [17]

15*4+100

15+15+15+15 = 60

60+100 =

$160

7 0
3 years ago
Read 2 more answers
Use the Distributive Property on 45x-6
Alexandra [31]

Answer:

<h3>180</h3>

Step-by-step explanation:

<h3>45 × -6 = 45 × [10+(-6)]</h3><h3>45 × (10-6)</h3><h3>45 × 4</h3><h3>180</h3>
5 0
3 years ago
Whats the answer for taking its square root?<img src="https://tex.z-dn.net/?f=y%5E%7B2%7D%20%3D%2068" id="TexFormula1" title="y^
Reil [10]

Answer:

y=\pm 2\sqrt{17}

Step-by-step explanation:

y=\pm \sqrt{68} \\ \\ y=\pm 2\sqrt{17}

4 0
1 year ago
Other questions:
  • Evaluate the expression when x = 3 and y=-7.<br> x-8y
    15·1 answer
  • Bryan paid a sale price of $45 for a video game. What is the original price if the discount was 25% off?
    14·1 answer
  • How to multiply a whole number with a mixed number?
    9·1 answer
  • Which transformation will map figure K onto figure K'? Two congruent kites figure K and figure K prime are drawn on a coordinate
    11·1 answer
  • Ten students enter a math contest. In how many ways can 1st, 2nd, and 3rd place trophies be awarded?
    13·1 answer
  • write the following expression as a multiple of the sum of two whole numbers with no common factor 54 + 78​
    10·1 answer
  • Which statement is true about this equation? -9(x + 3) + 12 = -3(2x + 5) − 3x
    11·1 answer
  • Find the value of the following expression
    5·1 answer
  • I need help with this im new to this i wasn’t at school theses days and my teacher won’t explain 2 me if u could help it would m
    10·1 answer
  • This graph shows the solution to which inequality?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!