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
5x+14-2x=9-(4x+2) can someone help
nekit [7.7K]
5x+14-2x=9-(4x+2)

3x+14=9-4x-2

3x+14=7-4x

7x+14=7

7x=-7

x=-1

Final answer: x=-1
5 0
3 years ago
What is the value of   for x = 2 and y = –4?
Nata [24]
The answer or value to this question will be D
6 0
3 years ago
Need help nowwww!!! With 1 threw 8
JulijaS [17]

1. B

2. B

3.C

4.B

5.B

6.A

6 0
3 years ago
A quadratic equation function f(x)=ax^2 passes through (0,0) and (5,5). write an equation for this function
Alex
Equation: f(x)=(1/5)x^2 or f(x)=(0.2)x^2

Check:
f(0)=(1/5)(0)^2
f(0)=(1/5)(0)
f(0)=0✓
f(5)=(1/5)(5)^2
f(5)=(1/5)(25)
f(5)=5✓
6 0
3 years ago
suppose you have three consecutive integers. The greatest of the three integers is twice as great as the sum of the first two. W
zvonat [6]

Answer:

0,1,2

Step-by-step explanation:

(x+2) = 2((x+1)+(x)

x+2 = 2x+2+2x

x+2 = 4x+2

-x       -x

2     = 3x + 2

-2            -2

0/3   = 3x/3

0 = x

6 0
3 years ago
Other questions:
  • Give an example of a linear equation in one variable with no solution. Explain how you know it has no solution.
    7·2 answers
  • Jada has a scale map of kansas that fits on a page in her book. The page is 5 inches by 8 inches. Kansas is about 210 miles by 4
    9·2 answers
  • What number is 20% of 700​
    13·2 answers
  • Which number is a multiple of 7
    8·1 answer
  • 31. Algebra Fill in the reason that justifies each step.
    6·1 answer
  • What does 74 divided by 8 equal
    14·2 answers
  • If 2x+15= 30<br> then what is x?
    10·2 answers
  • I need help asap due now
    7·1 answer
  • I need help, the question is “What is the slope, m, and y-intercept for the line that is plotted on the grid below?”
    6·1 answer
  • Please help me with this problem
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!