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galben [10]
1 year ago
6

The number of bacteria in a petri dish on the first day was 113 cells. If the number of bacteria increase at a rate of 82% per d

ay, how many bacteria cells will there be after 7 days?
Mathematics
1 answer:
Tresset [83]1 year ago
3 0

Answer:

4107 cells

Step-by-step explanation:

From the question, we have the following values:

Day 1 : 113 cells

Number of cells increases by day by 82%

Hence,

Day 2

113 × 82% = 92.66cells

Hence, Total number of bacteria cells for Day 2 = 113 + 92.66 = 205.66cells

Day 3

205.66 × 82% = 168.6412 cells

Hence, Total number of bacteria cells for Day 3 = 168.6412 + 205.66 = 374.3012 cells

Day 4

374.3012 × 82% = 306.926984 cells

Hence, Total number of bacteria cells for Day 4 = 306.926984 + 374.3012 = 681.228184 cells

Day 5

681.228184 × 82% = 558.60711088 cells

Hence, Total number of bacteria cells for Day 5 = 558.60711088 + 681.228184 = 1239.8352949 cells

Day 6

1239.8352949 × 82% = 1016.6649418 cells

Hence, Total number of bacteria cells for Day 5 = 1016.6649418 + 1239.8352949 = 2256.5002367 cells

Day 7

2256.5002367 × 82% = 1850.3301941 cells

Hence, Total number of bacteria cells for Day 7 = 1850.3301941 + 2256.5002367 = 4106.8304308 cells

Approximately to nearest whole number, the total number of bacteria cells that would be present after 7 days = 4107 cells

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Solve the given initial value problem and determine how the interval in which the solution exists depends on the initial value y
zalisa [80]

Answer:

y has a finite solution for any value y_0 ≠ 0.

Step-by-step explanation:

Given the differential equation

y' + y³ = 0

We can rewrite this as

dy/dx + y³ = 0

Multiplying through by dx

dy + y³dx = 0

Divide through by y³, we have

dy/y³ + dx = 0

dy/y³ = -dx

Integrating both sides

-1/(2y²) = - x + c

Multiplying through by -1, we have

1/(2y²) = x + C (Where C = -c)

Applying the initial condition y(0) = y_0, put x = 0, and y = y_0

1/(2y_0²) = 0 + C

C = 1/(2y_0²)

So

1/(2y²) = x + 1/(2y_0²)

2y² = 1/[x + 1/(2y_0²)]

y² = 1/[2x + 1/(y_0²)]

y = 1/[2x + 1/(y_0²)]½

This is the required solution to the initial value problem.

The interval of the solution depends on the value of y_0. There are infinitely many solutions for y_0 assumes a real number.

For y_0 = 0, the solution has an expression 1/0, which makes the solution infinite.

With this, y has a finite solution for any value y_0 ≠ 0.

8 0
2 years ago
Use the graph to determine the input values that correspond with f(x) = 1. x = 4 x = 1 and x = 4 x = −7 and x = 4 x = −7 and x =
Roman55 [17]

Answer:

x = −7 and x = 2

Step-by-step explanation:

This graph has two input values that will give an output of one

4 0
2 years ago
Read 2 more answers
A veterinarian needs to know an animal's weight in kilograms.If 20 pounds is about 9 kilograms and dog weighs 30 pounds,use a ra
Lesechka [4]

Answer:

Using the ratio table the dogs weight is:

30 pounds = 13.5 kilograms

Step-by-step explanation:

For this case we have the following conversion:

20 pounds = 9 kilograms

To use the table what we must do is find another relationship that allows us to find the weight in kilograms for 30 pounds.

For example, half the weight in pounds is half the weight in kilograms.

Therefore, the given conversion is:

10 pounds = 4.5 kilograms

So, for 30 pounds, we multiply this last ratio obtained by three on both sides:

30 pounds = 13.5 kilograms

Then, the table is:

Pounds 10 20 30

7 0
1 year ago
What property describes the number sentence 6+0=6
finlep [7]
The correct answer is: Additive identity property

Explanation:
<span>Additive identity property says that if zero is added to any real number, the resultant would be the same real number.

For Example:
6+0 = 6
 
In this case, we have added zero to a real number (6) and got that same real number (6) in return.</span>
3 0
2 years ago
Read 2 more answers
A high percentage of people who fracture or dislocate a bone see a doctor for that condition. Suppose the percentage is 99%. Con
marishachu [46]

Answer:

(i) 0.15708

(ii) 0.432488

(iii) 3

Step-by-step explanation:

Given that, 99% of people who fracture or dislocate a bone see a doctor for that condition.

There is only two chance either the person having fracture or dislocation of bone will either see the doctor or not.

As per previous data, if one person got a fracture or dislocation of bone, the chance of seeing the doctor is 0.99. Assuming this chance is the same for every individual, so the total number of people having fractured or dislocated a bone can be considered as Bernoulli's population.

Let p be the probability of success represented by the chances of not seeing a doctor by any one individual having fractured or dislocated a bone.

So, p=1-0.99=0.01

According to Bernoulli's theorem, the probability of exactly r success among the total of n randomly selected from Bernoulli's population is

P(r)=\binom{n}{r}p^r(1-p)^{n-r}\cdots(i)

(i) The total number of persons randomly selected, n=400.

The probability that exactly 5 of them did not see a doctor

So, r=5 , p=0.01

Using equation (i),

P(r=5)=\binom{400}{5}(0.01)^5(1-0.01)^{400-5}

=\frac{400!}{(400-5)!\times 5!}(0.01)^5(0.99)^{395}

=0.15708

(ii) The probability that fewer than four of them did not see a doctor

=P(r

=P(r=0)+P(r=1)+P(r=2)+P(r=3)

=\binom{400}{0}(0.01)^0(0.99)^{400}+\binom{400}{1}(0.01)^1(0.99)^{399}+\binom{400}{2}(0.01)^2(0.99)^{398}+\binom{400}{3}(0.01)^3(0.99)^{397}

=0.017951+0.072527+0.146154+0.195856

=0.432488

(iii) The expected number of people who would not see a doctor

=np

=300\times 0.01

=3

7 0
2 years ago
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