A bacteria culture grows with constant relative growth rate. The bacteria count was 2,560 after 4 hours and 2,621,440 after 12 hours.
(a) What is the relative growth rate? Express your answer as a percentage. (Round your answer to two decimal places.)
% per hr
(b) What was the initial size of the culture?
bacteria
(c) Find an expression for the exact number of bacteria after t hours, (t).
y(t) =
(d) Find the number of bacteria after 5.5 hours. (Round your answer to the nearest whole number.)
bacteria
(e) Find the rate of growth in bacteria per hour) after 5.5 hours. (Round your answer to the nearest whole number.)
bacteria per hour
(f) How many hours did it take for the population to reach 104,000? (Round your answer to two decimal places.)
hr

Answers

Answer 1

Answer:

A. 86.64%

B. 80

C. y(t)= 80[tex]e^{0.8664t}[/tex]

D. y(5.5) = 9388

E. y(t) = 8134 bacteria for every hour

F.  8.28 hours

Step-by-step explanation:

a. The bacteria count after 4 hours y(4) = 2560

The bacteria count after 12 hours y(12) = 2621440

equation 1: ye^4k = 2560

equation 2: ye^12k= 2621440

divide (2) by (1),

e^8k = 1024

Taking ln both sides:

ln(e8k ) = ln(1024)

8k = 6.931

k=0.8664      // after dividing both sides by 8

rate of growth k% = 0.8664*100 = 86.64%

b. substituting for k in equation 2:

   ye^4*0.8664 = 2560

   Initial bacteria count y(4) = 80

c. y(t)= 80e^0.8664t

d. the number of bacteria after 5.5 hours => y(5.5) = 80[tex]e^{0.8664(5.5)}[/tex] ≈ 9388

e. y'(5.5) = 80*0.8664e^0.8664(5.5) = 69.31e^0.8664(5.5) = 8134

f. for bacteria population = 104000

where ye^0.8664t = 104000

   y = 80

   80e^0.8664t = 104000    //divide both sides by 80

   e^0.8664t = 1300

   ln(e^0.8664t = ln(1300)

   t = 7.17 / 0.8664 = 8.28 hours


Related Questions

A transformation is given by the rule (x,y) → (x +3, y - 8). Which of the following describes the effect of this transformation on an object
A a translation by 8 units left and 3 units up
B a rotation by 90 counterclockwise about the origin
C a translation by 3 units right and 8 units down
D a reflection across the line 2 = 3

Answers

Answer:

3

Step-by-step explanation:

Answer:

C a translation by 3 units right and 8 units down

Step-by-step explanation: This answers the Unit 3 summative assessment N-gen Math

Find X HELP ME please!!

Answers

Answer:

The answer is A) 3 Hope this helped

Find the value of x.
(8x+19)(9x+9)
Please give step by step

Answers

SOLUTION STEPS

(8x+19)(9x+9)

Apply the distributive property by multiplying each term of 8x+19 by each term of 9x+9.

72x 2 +72x+171x+171

Combine 72x and 171x to get 243x.

72x 2 +243x+171

hopefully my weird explanation helped

Bart read 3,432 pages of books last year! That's 1,544 fewer pages than he read the year before. How many pages did Bart read in the two years combined?​

Answers

Answer:

5,320 pages

Step-by-step explanation:

Last year: 3,432 pages

Last year: 3,432-1,544= 1,888

3,432+1,888= 5,320

If you have 2 pieces of spaghetti that have lengths 4 cm and 10 cm, what could be the possible length of a third piece of spaghetti to complete the triangle? cm < x < cm

Answers

Answer:

  6  <   third side    <   14

Third side must be greater than 6 and less than 14

Step-by-step explanation:

A triangle can be formed from 2 sides of any length.

The third side must be longer than the difference of the other 2 sides and

the third side must be less than the sum of the other 2 sides.

(if this question is from k12 lesson check)

Please answer ASAP I have 15 min help

Answers

she did not follow PUMAS...

this means she added before multiplying or dividing

Answer:

32

Step-by-step explanation:

she was supposed to divide and multiply first and then add those answers

6+6+20=32

While printing material from the Internet, Greg used 10 pages of paper from a package of 500 sheets of paper. What percent of the paper did he use?

Answers

Answer:

2%

Step-by-step explanation:

The percentage of paper used is 2%

given the function f(x)= 3^ - 2 what is the value of f (3)

Answers

I am assuming you meant to write f(x) = 3^x -2

f(3) = 3^3 - 2 <=>

f(3) = 27 - 2 <=>

f(3) = 25

1/2^-2 2^-3 -4^5
What is the value of
for x = 2 and y=-4?

Answers

value of x=2 is-8 and y=-4 is -1024

True or False: The Commutative Property of Addition states that for all expressions a and b , ab = ba.

Answers

According to the Commutative Property of Addition, ab = ba for all expressions a and b: FALSE

What is the Commutative Property of Addition?According to the commutative property of addition, altering the order of addends has no impact on the sum. Here's an illustration: 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+4. The addition and multiplication arithmetic operations are covered by the commutative property. This implies that the outcome of adding or multiplying two numbers remains unchanged if the order or position of the numbers is changed. For instance, 4 + 5 equals 9, and 5 + 4 equals 9.

According to the Commutative Property of Addition, rearranging the addends has no impact on the sum.

a+b=b+a

Therefore, the statement "according to the Commutative Property of Addition, ab = ba for all expressions a and b" is FALSE

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Select two ratios that are equivalent to 2:9

Choose 2 correct answers

Answers

Answer:

4:18 and 6:27

Step-by-step explanation:

Jana ran the first 312 miles of a 5-mile race in 13 hours. What was her average rate, in miles per hour, for this first part of the race? Explain how you solved the problem.

Answers

Answer:

speed = distance / time

Jana's speed is

  speed = (3.5 mi)/(1/3 h) = 3*3.5 mi/h = 10.5 mi/h

x
y
-3
6
-1
4.
0
3
1
3
3
4
3
6

Answers

it’s not good to solve

three orders are placed at a pizza shop.
two small pizzas, a liter of soda, and a salad costs $14.
one small pizza, a liter of soda, and three salads costs $15.
three small pizzas, a liter of soda, and two salads costs $22.
how much does each item cost?

Answers

Given:

Two small pizzas, a liter of soda, and a salad costs $14.

One small pizza, a liter of soda, and three salads costs $15.

Three small pizzas, a liter of soda, and two salads costs $22.

To find:

The cost of each item.

Solution:

Let x be the cost of a small pizza.

y be the cost of a liter of soda

z be the cost of a salad.

According to the question, two small pizzas, a liter of soda, and a salad costs $14.

[tex]2x+y+z=14[/tex]           ...(i)

One small pizza, a liter of soda, and three salads costs $15.

[tex]x+y+3z=15[/tex]         ...(ii)

Three small pizzas, a liter of soda, and two salads costs $22.

[tex]3x+y+2z=22[/tex]      ...(iii)

From (i), we get

[tex]z=14-2x-y[/tex]        ...(iv)

Putting [tex]z=14-2x-y[/tex] in (ii), we get

[tex]x+y+3(14-2x-y)=15[/tex]

[tex]x+y+42-6x-3y=15[/tex]

[tex]-5x-2y=15-42[/tex]

[tex]-(5x+2y)=-27[/tex]

[tex]5x+2y=27[/tex]            ...(v)

Putting [tex]z=14-2x-y[/tex] in (iii), we get

[tex]3x+y+2(14-2x-y)=22[/tex]

[tex]3x+y+28-4x-2y=22[/tex]

[tex]-x-y=22-28[/tex]

[tex]-(x+y)=-6[/tex]

[tex]x+y=6[/tex]

Multiply both sides by 2.

[tex]2x+2y=12[/tex]    ..(vi)

Subtracting (vi) from (v), we get

[tex]5x+2y-2x-2y=27-12[/tex]

[tex]3x=15[/tex]

[tex]x=5[/tex]

Putting x=5 in (vi), we get

[tex]2(5)+2y=12[/tex]

[tex]10+2y=12[/tex]

[tex]2y=12-10[/tex]

[tex]2y=2[/tex]

[tex]y=1[/tex]

Putting x=5 and y=1 in (iv), we get

[tex]z=14-2(5)-(1)[/tex]

[tex]z=14-10-1[/tex]

[tex]z=3[/tex]

So, [tex]x=5,y=1,z=3[/tex].

Therefore, the cost of a pizza is $5, cost of a liter of soda is $1 and cost of salad is $3.

Jace and his children went into a bakery and he bought $9 worth of cookies and brownies. Each cookie costs $0.75 and each brownie costs $3. He bought twice as many cookies as brownies. Graphically solve a system of equations in order to determine the number of cookies, x,x, and the number of brownies, y,y, that Jace bought.

Answers

Answer:

(9, 18) (3, 6) Plz correct me if wrong

Step-by-step explanation:

Jace bought 4 cookies and 2 brownies from the bakery.

Let x represent the number of cookies and y represent the number of brownies.

Since he bought $9 worth of cookies and brownies. Each cookie costs $0.75 and each brownie costs $3. hence:

0.75x + 3y = 9      (1)

Also, he bought twice as many cookies as brownies, hence:

x = 2y

x - 2y = 0     (2)

Solving equation 1 and 2 simultaneously gives x = 4, y = 2

Hence Jace bought 4 cookies and 2 brownies from the bakery.

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NEED HELP! GIVING BRAINLIEST!

Answers

A, in one day there are 6 clients and for each day multiplied it equals C for example if you were to plug in 1 for d
6(1)=6 and so on which shows the total clients.

WILL MARK BRAINLIEST!!

Answers

Answer:

only p(x)

Step-by-step explanation:

The others have a restricter domain

Solve the following system of equations. x + y + 8z = 16
2x + 7z = 19
4x - 4y + 4z = 4

a. x = 1,y = 2,z = 2
b. x= 2,y = 2,z = 1
c. x = 6,y = 2,z = 1
d. x = 13,y = 11,z = -1​

Answers

By substitution, we will see that the solution of the system is:

x = 13, y = 11, z = -1

The correct option is D.

How to solve the system of equations?

Here we have a system of 3 equations:

x + y + 8z = 16

2x + 7z = 19

4x - 4y + 4z = 4

I will solve it by substitution, first, let's simplify the equations. Here we can divide the third equation by 4 so we remove all the common factors, then the system becomes:

x + y + 8z = 16

2x + 7z = 19

x - y + z = 1

Now, I will isolate x on the second equation:

x = (19 - 7z)/2 = (19/2) - (7/2)*z = 9.5 - 3.5*z

Now we can replace that on the other two equations:

(9.5 - 3.5*z) + y + 8z = 16

(9.5 - 3.5*z) - y + z = 1

Rewriting the system we get:

y + 4.5z = 6.5

-y - 2.5z = -8.5

Now we can isolate y on the first equation:

y = 6.5 - 4.5z

Replacing that on the other equation we get:

-(  6.5 - 4.5z) - 2.5z = -8.5

-6.5 + 4.5z - 2.5z = -8.5

2z = -8.5 + 6.5 = -2

z = -2/2 = -1

Then the value of y is:

y = 6.5 - 4.5z = 6.5 - 4.5*(-1) = 11

And the value of x is:

x = 9.5 - 3.5*z = 9.5 - 3.5*(-1) = 13

So the solution of the system is:

x = 13, y = 11, z = -1

The correct option is D.

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Larry ordered 5 1/2 subs. He wants to share the subs with 4 friends and himself. Larry thinks they will each
receive 1 1/4 subs. Is Larry correct? Why or why not?

Answers

Larry is incorrect if every person received 1 1/4 of a sub he would need at least 6.25 subs

find the factorization of the polynomial below 49x2+70+25

Answers

Answer:

(7x + 5) (7x+5)

Step-by-step explanation:

Hope this helps

The rabbit population in a certain area is 200% of last years population there are 1,100 rabbits this year, how many were there last year?​

Answers

Answer:

550

Step-by-step explanation:

1100/2=550

(can I get brainliest please)

Marion and Stefan played a game called "Go." Marion won five times the difference between the number of games Stefan won and the number four. If Marion won fifteen games, then how many games did Stefan win?

Answers

Answer:

1 game

15/5=3

4-3=1

Hope it helps

please follow me

Using a system of equations, it is found that Stefan won 7 games.

In our system, we have that:

x is the number of games Marion won.y is the number of games Stefan won.

Marion won five times the difference between the number of games Stefan won and the number four, hence:

[tex]x = 5(y - 4)[/tex]

Marion won 15 games, hence [tex]x = 15[/tex], and:

[tex]15 = 5(y - 4)[/tex]

[tex]y - 4 = 3[/tex]

[tex]y = 7[/tex]

Stefan won 7 games.

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Question 2
1 pts
Seven friends compared vacation plans. All are planning to drive to their destinations.
Find the median distance for the seven travelers.
Distance in
Friend
km
1
435
2
158
3
254
450
4
5
192
219
6
7
457
192 km

Answers

i think the answer is the median is 236.5

Solve the equation Only enter the amount. Round to the nearest cent. Twenty tickets cost 182.50 What is the average cost of each ticket?

Answers

Answer:

$9.13

Step-by-step explanation:

The deer population is estimated to be 17,600 in northern Illinois, but an actual count was 21,300. What is the percent error? 1 point 82.6% 21% 20% 17.4% Last week, you finished Hurry

Answers

Answer:67

Step-by-step explanation: 82.6% is over 49

What is the distance between the points (2, 1) and (14, 6) on a coordinate
plane?

Answers

9514 1404 393

Answer:

  13 units

Step-by-step explanation:

The distance is found using the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((14 -2)² +(6 -1)²) = √(144 +25) = 13

The distance between the two points is 13 units.

Find the volume of this right rectangular prism. [Type your answer as a number.]

Answers

Answer:

200m

Step-by-step explanation:

To find volume you multiply each side, length, width, and height. 5 times 4 is 20, and 20 times 10 is 200

A deposit of $225 as an integer

Answers

Answer:

225

Step-by-step explanation:

A deposit is positive, so a deposit of $225 as an integer (number) would be 225

I hope this helps!

A flagpole casts a shadow that is 24 ft long at the same time you cast a shadow that is
4.5 ft long. If you are 6 ft tall, how tall is the flagpole?

Answers

Answer:

32 ft tall

Step-by-step explanation:

24 divided by 4.5 is 5.3 repeating. 6 times 5.3 is around 32

I need to know the answer lol

Answers

the orange one , 5/12

hope this helps! please mark brainliest :)

Answer:

5/12

Step-by-step explanation:

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