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
horsena [70]
3 years ago
8

A scientist is testing a new antibiotic by applying the antibiotic to a colony of 10,000 bacteria. The number of bacteria decrea

ses by 75% every two hours. How many hours will it take for the bacteria colony to decrease to 1000? Round your answer to the nearest tenth of an hour.
Mathematics
1 answer:
artcher [175]3 years ago
8 0

Answer:

3.3 hours.

Step-by-step explanation:

We have been given that a scientist is testing a new antibiotic by applying the antibiotic to a colony of 10,000 bacteria. The number of bacteria decreases by 75% every two hours.

Since number of bacteria is decreasing exponentially, so we will use exponential decay function.

y=a*b^x, where,

a= Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

75\%=\frac{75}{100}=0.75

As number of bacteria is decreasing every 2 hours, so number of bacteria decreased in 1 hour will be x/2.

Upon substituting our given values in above formula we will get,

y=10,000(1-0.75)^{\frac{x}{2}}

To find the number of hours it will take to for the bacteria colony to decrease to 1000, we will substitute y = 1,000 in our equation.

1,000=10,000(0.25)^{\frac{x}{2}}

Let us divide both sides of our equation by 10,000.

\frac{1,000}{10,000}=\frac{10,000(0.25)^{\frac{x}{2}}}{10,000}

0.1=(0.25)^{\frac{x}{2}}  

Let us take natural log of both sides of our equation.

ln(0.1)=ln((0.25)^{\frac{x}{2}})

ln(0.1)=\frac{x}{2}*ln(0.25)

-2.302585=\frac{x}{2}*-1.386294

x=\frac{-2.302585}{-1.386294}*2

x=1.660964*2

x=3.3219\approx 3.3

Therefore, it will take 3.3 hours  for the bacteria colony to decrease to 1000.

You might be interested in
Help me quick.............................
almond37 [142]

Answer:

angle 5 and angle 4.

Step-by-step explanation:

complementary angles are the sum of two angles that equal 90 degrees

6 0
3 years ago
Elena’s bedroom door is 0.8 m wide. How wide should the door be on the scale drawing, if the ratio is 1 to 50?
arlik [135]

We are given Elena’s bedroom door's width = 0.8 m.

Also the scale drawing is in the ratio of 1 to 50 that is 1/50.

<em>In order to find the width of  scale drawing, we need to multiply original width of the door by 1/50.</em>

If we multiply 0.8 by 1/50, we get

0.8 × 1/50 = 0.8/50 = 0.016 meter.

So, we can say 0.016 meter wide should the door be on the scale drawing, if the ratio is 1 to 50.


7 0
3 years ago
Read 2 more answers
Brian compared the absolute values of the numbers−12,34,and−14.Arrange the numbers from least to greatest.
solniwko [45]

Answer:

-12, -14, 34

Step-by-step explanation:

3 0
3 years ago
What issues does a person "charged" with a crime typically have to deal with?
GuDViN [60]
Possible facing a jury and being healed in jail, hiring a layer and going to court
7 0
3 years ago
Read 2 more answers
What is the volume of a cone with a radius of 4 centimeters and a height of 5 centimeters?
Salsk061 [2.6K]
Volume of a cone: 1/3*pi*4*4*5 = 83.776 cubic cm rounded up to 3 decimal places
3 0
3 years ago
Other questions:
  • I need help with my math question please will give brainlest answer award...
    13·2 answers
  • Find the exact value of cos(arcsin( one fourth )). For full credit, explain your reasoning. (2 points)
    7·1 answer
  • 20 POINTS, and BRAINIEST
    9·2 answers
  • The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 mi
    12·1 answer
  • A ladder leans against the side of the house. The angle of elevation of the ladder is 61 degrees when the bottom of the ladder i
    14·1 answer
  • Help please? I don’t get math at all
    7·1 answer
  • What is the value of x?
    13·1 answer
  • <img src="https://tex.z-dn.net/?f=%5Chuge%5Cbold%5Cred%7B%7BHELP%7D%7D" id="TexFormula1" title="\huge\bold\red{{HELP}}" alt="\hu
    11·1 answer
  • How to find the answer to0.291×0.34
    12·2 answers
  • when comparing condition means in an experiment with more than two conditions, why should you use an analysis of variance instea
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!