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
kvv77 [185]
3 years ago
9

In a research lab, a cell biologist is growing a strain of bacteria under two different conditions. Culture A had an initial pop

ulation of 200 and doubles every hour. Culture B had an initial population of 819200 but has been contaminated. Its population is now decreasing by half every hour. When will the two cultures have an equivalent population? Solve using an exponential equation.
Mathematics
1 answer:
zhannawk [14.2K]3 years ago
3 0

Answer:

They will have the same population after 6 hours

Step-by-step explanation:

The general exponential equation format for this is;

P = P_o(e^(kt))

For Culture A, we are told that it had an initial population of 200 and doubles every hour.

Thus;

After 1 hour, P = 400

After 2 hours, P = 800

After 3 hours, P = 1600

Thus;

At t = 1, we have;

400 = 200(e^(k × 1))

400/200 = e^(k)

e^(k) = 2 - - - (eq 1)

At t = 2, we have;

800 = 200(e^(k × 2))

800/200 = e^(2k)

e^(2k) = 4 - - - (eq 2)

To find k, let's divide eq 1 by eq 2.

(e^(2k))/e^(k) = 4/2

e^(2k - k) = 2

e^(k) = 2

k = In 2

k = 0.6931

Thus;

P = 200e^(0.6931t)

For Culture B, we are told that it had an initial population of 819200 but has been contaminated. Its population is now decreasing by half every hour.

Thus;

After 1 hour, P = 409600

After 2 hours, P = 204800

After 3 hours, P = 102400

Thus;

At t = 1, we have;

409600 = 819200(e^(k × 1))

409600/819200 = e^(k)

e^(k) = 0.5 - - - (eq 1)

At t = 2, we have;

204800 = 819200(e^(k × 2))

204800/819200 = e^(2k)

e^(2k) = 0.25 - - - (eq 2)

To find k, let's divide eq 1 by eq 2.

(e^(2k))/e^(k) = 0.25/0.5

e^(k) = 0.5

k = In 0.5

k = -0.6931

Thus;

P = 819200(e^(-0.6931t))

We want to find the time when the 2 cultures will have the same population. Thus;

200e^(0.6931t) = 819200(e^(-0.6931t))

Arranging, we have;

(e^(0.6931t))/(e^(-0.6931t)) = 819200/200

e^(0.6931t - (-0.6931t) = 4096

e^(1.3862t) = 4096

1.3862t = In 4096

1.3862t = 8.3178

t = 8.3178/1.3862

t ≈ 6 hours

You might be interested in
A magazine publisher mails a survey to every subscriber asking about the quality of its subscription service.
scoray [572]
A Statistic.

Since they want to know how their magazine are, they are gonna make a survey. In the survey, the people are statistics to see how well their magazines are. With that, they can decide to change their subjects or whatever it is. Hope this helps!
3 0
3 years ago
What is the mean of the data set in the box below?<br> -8, -6, - 2, 0, -6, - 8. 4, 7, 8, 1
Andreas93 [3]
The mean of the data set in the box below is -1
3 0
3 years ago
Definición de forma estándar y ejemplo????
defon

Answer:

Las reglas para escribir un número en forma estándar es que primero escribes un número entre 1 y 10, luego escribes × 10 (a la potencia de un número). En una calculadora, generalmente ingresa un número en forma estándar de la siguiente manera: Escriba el primer número (el que está entre 1 y 10). Presione EXP

Step-by-step explanation:

3 0
3 years ago
Can somebody plz help answer this word problem (showing the steps to get answer) thanks!
Alex

Answer:

528 cookies

Step-by-step explanation:

3 hours 55 minutes

=3×60+55

=235 and

235-215 ( for preheating minutes)

220

So

20 minutes…=48 cookies

1. ". =48/20 "

220 ". =48/20×220 "

=12/5×220 "

= 528 "

8 0
3 years ago
Read 2 more answers
Find m&lt;5=<br>and m&lt;7= <br>PLEASE HELP BRAINLIEST ​
Rudik [331]

Answer:

angle 5 = angle 7 = 127°

Step-by-step explanation:

here , in the given figure ;

angle 2 + angle 5 = 180°

( pair of co-interior angles )

so, 53° + angle 5 = 180°

=》angle 5 = 180° - 53° = 127°

hence angle 5 = 127°

and angle 5 = angle 7 ( vertical opposite angles )

so, angle 5 = angle 7 = 127°

7 0
3 years ago
Read 2 more answers
Other questions:
  • The compound inequality could represent which scenario? If Janie scores between 8.3 and 9.8 in her gymnastics performance, she q
    13·2 answers
  • Clare earned a total of $12 for 2 hours of yard work. How many hours in all will it take Clare
    15·1 answer
  • In hyperbolic geometry, a triangle could potentially have ___ degrees.
    11·2 answers
  • The function f is defined by f(x)=200÷x−b, where b is a constant. Find b, if the value of f at x= 1/3 is equal to 150.
    12·1 answer
  • 1 1/6 • 20 13/24 =? What is the answer to this?
    9·1 answer
  • Simplify any fractions ! will mark as brainliest!
    10·2 answers
  • out of 18 people in the glee club, 11 have dogs and 7 have cats. four people have both cats and dogs. how many club members have
    13·2 answers
  • For each logarithmic equation, write an equivalent equation in exponential form
    13·1 answer
  • on a map 1 in. = 25 meters. the distance between school and the post office is 23 inches on the map. what is their actual distan
    10·1 answer
  • A parabola can be drawn given a focus of (-11, -2) and a directrix of x= -3
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!