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
Alexandra [31]
2 years ago
13

A bacteria culture starts with 660 bacteria and grows at a rate proportional to its size. After 6 hours there will be 3960 bacte

ria. (a) Express the population after t hours as a function of t. population: (function of t) (b) What will be the population after 3 hours?
Mathematics
1 answer:
scoray [572]2 years ago
4 0

Answer:

a) P(t) = 660 e^{\frac{ln(6)}{6} t}

b) P(t=3) = 660 e^{\frac{ln(6)}{6}*3} = 1616.663 \approx 1617

Step-by-step explanation:

For this case we have the following info:

P(0) = 660 represent the initial amount of bacteria

P(6) = 3960 represent the population of bacteria after 6 hours

Part a

For this case we use the proportional model given by:

\frac{dP}{dt}= kP

Where P represent the population at time t and k is a constant of proportionality.

We can rewrite the model like this:

\frac{dP}{P} = k dt

And if we integrate both sides we got:

ln |P|= kt + C

Now if we apply exponential we got:

P = e^{kt +c}= e^{kt} e^C

P(t)= P_o e^{kt}

For this case using the initial condition:

660 = P_o e^{0k}, P_o = 660

We have the following model:

P(t) = 660 e^{kt}

Using the second condition P(6) = 3960 we have this:

3960 = 660e^{6k}

We can divide both sides by 660 and we got:

6= e^{6k}

Now we can apply natural log on both sides and we got:

ln (6)= 6k

k = \frac{ln(6)}{6}=0.2986265782

So then the model would be given by:

P(t) = 660 e^{\frac{ln(6)}{6} t}

Part b

For this case we just need to replace t=3 into the model and we got:

P(t=3) = 660 e^{\frac{ln(6)}{6}*3} = 1616.663 \approx 1617

You might be interested in
XClusive! Why or why not?
Furkat [3]

wearing because of the division of running man.

Step-by-step explanation:

The statistics are divided by 29 to get the answer in cubic cm.

6 0
2 years ago
Hello i need urgent help with this assignment.
Mars2501 [29]

Answer:

AD = 1 3/4y + 5/8x - 3

Step-by-step explanation:

AD = 1/4x + 2y + 3 - 1/4y + 3/8x - 6

combine like terms:

AD = 1 3/4y + 5/8x - 3

7 0
2 years ago
Read 2 more answers
The perimeter of a triangle is 30 units. If it is dilated with respect to origin by a scale factor of 0.5, what is the perimeter
il63 [147K]
<span>Choices: 30 units ; 20 units ; 15 units ;  7.5 units

Given:
perimeter = 30 units
scale factor = 0.5

30 units * 0.50 = 15 units

The perimeter of the resulting triangle is 15 units.</span>
6 0
3 years ago
A tarp is used to keep the infield of a baseball field from getting wet. The infield is a square. The corners of the square tarp
Dafna11 [192]

Answer:

<h2>a. 2,025 ft</h2><h2>b. 8,100 is a perfect square. </h2>

Step-by-step & explanation:

<em>It is a perfect square because if it wasn't, it wouldn't be equally a whole number when divided by 4 or 2,025 exactly on ALL 4 sides and when finding the root of 8,100 it's a perfect 90.  As you should already know a perfect square has a given 90 degree angle.</em>

Tarp = 8,100 sq ft.

- anchored corners at the base.

- Square infield.

Well if there's 4 bases, divide 8,100 by 4.

8,100 / 4 = 2,025

One base to another base is 2,025 ft.

8 0
3 years ago
What is the formula for the area of a triangle?
Semmy [17]

Answer:  c. (1/2) bc sin A

<u>Step-by-step explanation:</u>

You can find the area of a triangle using trigonometry if you know the lengths of two sides and the measure of the included angle using the following formula:

A=\dfrac{1}{2}ab\sin C

5 0
3 years ago
Read 2 more answers
Other questions:
  • There are 18 oranges in box A and 36 in box B. What is the ratio of the oranges in Box A to Box B?
    6·2 answers
  • Read the proof. Given: AB ∥ DE Prove: △ACB ~ △DCE We are given AB ∥ DE. Because the lines are parallel and segment CB crosses bo
    15·2 answers
  • How do i read a curve graph need help !!!
    12·1 answer
  • Using the drawing Below, find all the possible situations it could be describing. Mark all situations that apply to the inequali
    8·1 answer
  • An item sells for $40 . The sales tax on the item is 8%. What is the sales tax and total cost?
    6·1 answer
  • Enter a range of values for x please help me
    8·1 answer
  • Find the length of the third side to the nearest thenth
    7·1 answer
  • Write an explicit formula for the geometric sequence below and use it to find the 9th term. 256, 64, 16, 4, . . .
    9·1 answer
  • Sara and Sage are making hot cocoa. The tables below show the recipes each one used. Which recipe has the strongest chocolate fl
    15·2 answers
  • 18 × [ 7+(-3) ] = [ 18 x 7] + [ 18 × (-3) ]​
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!