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
andrew11 [14]
3 years ago
6

A population of protozoa develops with a constant relative growth rate of 0.6137 per member per day. On day zero the population

consists of six members. Find the population size after seven days.
Mathematics
1 answer:
Wewaii [24]3 years ago
7 0

Answer:

The population size after seven days will be 171.

Step-by-step explanation:

The population of protozoa can be modeled by the following equation.

Q(t) = Q(0)(1+r)^{t}

In which Q(t) is the population after t days, Q(0) is the initial population and r is the growth rate.

In this problem, we have that:

Q(0) = 6, r = 0.6137

So

Q(t) = 6(1.6137)^{t}

Find the population size after seven days.

This is Q(7).

Q(7) = 6(1.6137)^{7} = 171

The population size after seven days will be 171.

You might be interested in
Write an exponential equation to represent the situation and answer the question.
Gala2k [10]

Answer:

a. $4.48¢

b. 9,967 people

ci. Multiplier: F = 25 × (1.09)^t

cii. Percent increase = 9.15%

Step-by-step explanation:

a. The equation we are going to use to calculate the future cost of bread in 5 years:

P = F/(1+r)^t

Where P is current cost, F = future cost(what we are required to calculate), r = percentage increase per year, t = time (years).

Where P = 2.75

r = 5/100 or 0.05

t = 10

F = ?

Substituting appropriately, we have:

2.75/1 = F/(1+0.05)^10

We then cross multiply

F = 2.75 × (1+0.05)^10

F = 2.75 × (1.05)^10

F = 2.75 × 1.62889

F = $4.48¢

Therefore, the bread will cost $4.48 in 10 years.

b. Here population is 42,000 people now. There's predicted 25% decrease in population every year for the next 5years. We are to calculate the expected population in 5 years. The equation that can be used to calculate the expected population:

P = F/(1 - r)^t

F = future population

P = present population

r = percentage of decrement

t = period.

Here P = 42,000

r = 25/100 = 0.25

t = 5

F = ?

Substituting accordingly:

42000 = F/(1 - 0.25)^5

Cross multiply

F = 42000 × [(1 - 0.25)^5]

F = 42000 × 0.2373

F = 9,967

The population in the next 5 years will decrease to 9,967 people.

c. Share of orange stock = $25 in the year 2000

The same share = $60 in 2010, we are required to determine the multiplier and percent increase.

Since the future value = $60, the present value = $25, the time = 2010 - 2000 = 10 years. Then we can use the formula:-

F = P × (1 + r)^t

60 = 25 × (1 + r)^10

(1 + r)^10 = 60/25

(1 + r)^10 = 2.4

1 + r = 10√2.4

1 + r = 1.0915

r = 1.0915 - 1

r = 0.0915

r = 9.15%

Therefore the multiplier is:

F = 25 × (1.09)^t

The percent increase = 9.15%

8 0
3 years ago
As part of quality-control program, 3 light bulbs from each bath of 100 are tested. In how many ways can this test batch be chos
hichkok12 [17]

Answer:

<h3>By 161700 ways this test batch can be chosen.</h3>

Step-by-step explanation:

We are given that total number of bulbs are = 100.

Number of bulbs are tested = 3.

Please note, when order it not important, we apply combination.

Choosing 3 bulbs out of 100 don't need any specific order.

Therefore, applying combination formula for choosing 3 bulbs out of 100 bulbs.

^nCr = \frac{n!}{(n-r)!r!} read as r out of n.

Plugging n=100 and r=3 in above formula, we get

^100C3 = \frac{100!}{(100-3)!3!}

Expanding 100! upto 97!, we get

=\frac{100\times 99\times 98\times 97!}{97!3!}

Crossing out common 97! from top and bottom, we get

=\frac{100\times 99\times 98}{3!}

Expanding 3!, we get

=\frac{100\times 99\times 98}{3\times 2\times 1}

= 100 × 33  × 49

= 161700 ways.

<h3>Therefore,  by 161700 ways this test batch can be chosen.</h3>
3 0
4 years ago
What is the answer I need help
Advocard [28]

Answer:

A: distributive property

Step-by-step explanation:

Hopefully this helps!

4 0
3 years ago
Given that 5 miles is 8 km, convert 19.2 miles to km.​
Feliz [49]

Answer: 19.2 miles is 30.72 km

Step-by-step explanation:

Since 5 miles is 8 km, divide 8/5 to find out how many miles is one kilometer.

8/5 = 1.6

Multiply 19.2*1.6 to find out how many kilometers 19.2 miles is.

19.2*1.6 = 30.72

(Note that when you search it up online, 19.2 miles is actually 30.9 km, because 5 miles isn't exactly 8km!)

7 0
3 years ago
Help please. thank you
tatyana61 [14]
I think it D cause 30(cos(30x)+14=-16
Your dividing by 30
your 180 (which is degrees) is
radians. As the cosine function is periodic with period 2 we get

6 0
3 years ago
Read 2 more answers
Other questions:
  • Two taps A and B fill a swimming pool together in two hours. Alone, it takes tap A three hours less than B to fill the same pool
    14·2 answers
  • I need to know what is x ..................
    9·2 answers
  • According to one organization, there are about 93,600,000 pet cats and about 77,500,000 pet dogs in the U.S. Are there more pet
    8·2 answers
  • Twelve less than the quotient of a number and 7 is -2
    7·1 answer
  • The parallelogram shown below has an area of 54 units. find the missing height
    9·2 answers
  • What is formula of sec(A+B)​
    12·1 answer
  • Find the surface area of the solid. Round to two decimal places
    9·1 answer
  • Use the drawing tools to form the correct answer on the graph. Graph this function. - 2 + 8 = Reset ® Delet Undo Drawing Tools C
    14·1 answer
  • A certain cake recipe calls for 2 7/8 cups of sugar to make one cake, If you want to make four cakes, how many cups of sugar, do
    7·1 answer
  • Pls answer like this:<br> X= ___<br> And angle a = ___degrees.<br> 20 points!!!
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!