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
This is for homework its a fraction <br> x/5 = 3
kenny6666 [7]

Answer:

it is saying 5 divided by what equals three so I sugest to start by finding out what is half of 5

Step-by-step explanation:

5 0
3 years ago
How do you take the antiderivative of (sinxcosx)^2?
gtnhenbr [62]
<span>∫(sinx cosx)^2dx = ∫(1/2sin 2x)^2 dx = 1/4∫sin^2 2x dx = 1/4∫1/2(1 - cos 4x)dx = 1/8∫(1 - cos 4x) dx = 1/8[x - sin 4x / 4] + c = 1/32(4x - sin 4x) + c
</span>
8 0
3 years ago
Which equation is y = –3x2 – 12x – 2 rewritten in vertex form?
WARRIOR [948]
Y=-6-12x-2
y=-6-12x-2
y=-8-12x
y=-8-12x
and these are real numbers
7 0
3 years ago
Read 2 more answers
A straight line, L, is perpendicular to the straight line y=2x-1 and passes through the point (8,1). Find an equation of L
luda_lava [24]
Let's call that other line with the eqn. y=2x-1 line M.
This line is in slope-intercept form, which means that it is written in the form y=mx+b where m is the slope and b is the y-intercept.
This means that the slope of line M is 2.

Perpendicular lines have slopes which are opposite reciprocals.
(that is to say, if you flipped the fraction and changed the sign)

Of course, 2 isn't a fraction, but it's implied as 2/1.
The opposite reciprocal would then be -1/2.
Let's plug this into our slope-intercept form equation for line L.

y = mx + b
y = -1/2x + b

Of course, we still need to find that y-intercept. (y when x = 0)
To do this, we need to interpret the slope.
Slopes are rise over run, so m = -1/2 means a change of -1 in y = 2 in x.
Let's take a point we know is in our line, (8, 1).
To find that y-intercept, we want x to be 0.
To do this, we'd have to subtract 8 from x.
And according to our slope, this means adding 4 to y.
Our y-intercept is at (0, 5), with the value b that we use being just 5.

\boxed{y=-\frac{1}2x+5}
7 0
3 years ago
I need to factor each polynomial completely and show my work. 12-17 I need help solving these
Vinvika [58]
The answer to the questions

7 0
3 years ago
Other questions:
  • Please help me remember how to solve this equation: (13+x)².
    14·1 answer
  • Dahlia has just enough money to buy either 6pears and 20oranges or 12oranges and 11pears. A pear costs $0.80. How much does an o
    13·1 answer
  • Are the lines parallel, perpendicular, or neither
    15·1 answer
  • Mr. Flores charges $ 530 for car repairs to his credit card, which charges no interest if
    13·1 answer
  • Given: g(x)=1/x+2 and h(x)=3x Check all restrictions on the domain of gOh.
    13·2 answers
  • Factor by grouping. 4x^3 − 16x^2 + 12 − 3x
    14·1 answer
  • Which is greater than 4?(show work)<br> (a) 5,<br><br> (b) -5,<br><br> (c) -1/2,<br><br> (d) -25.
    8·1 answer
  • In the diagram, L1 is parallel to L2.
    8·1 answer
  • (10, y) and (3, 4); m = - 2/7​
    12·1 answer
  • Please help EDGINUITY 2022
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!