Suppose Y(t) = 25e^3t + 12 represents the number of bacteria present at time t minutes. At what time will the population reach 100 bacteria? ( Note: Answers are expressed in terms of natural logarithm

Answers

Answer 1

Given:

The given function is:

[tex]Y(t)=25e^{3t}+12[/tex]

Where Y represents the number of bacteria present at time t minutes.  

To find:

The time taken by bacteria population to reach 100 bacteria.

Solution:

We have,

[tex]Y(t)=25e^{3t}+12[/tex]

Putting [tex]Y(t)=100[/tex], we get

[tex]100=25e^{3t}+12[/tex]

[tex]100-12=25e^{3t}[/tex]

[tex]88=25e^{3t}[/tex]

Divide both sides by 25.

[tex]\dfrac{88}{25}=e^{3t}[/tex]

Taking ln on both sides, we get

[tex]\ln (\dfrac{88}{25})=\ln e^{3t}[/tex]

[tex]\ln(\dfrac{88}{25})=3t[/tex]                  [tex][\because \ln e^x=x][/tex]

Divide both sides by 3.

[tex]\dfrac{1}{3}\ln(\dfrac{88}{25})=t[/tex]

Therefore, the required time is [tex]\dfrac{1}{3}\ln(\dfrac{88}{25})[/tex] minutes.


Related Questions

Plz help me thanks

Complete the square to make a perfect square trinomial. Then, write a result as a binomial squared. m^2-13m

m^2-13+ ? =( ? )^2

Answers

Answer:

Look at the picture

Hope it helped!

Answer:   m^2 - 13m + 42.25  = (m - 6.5)^2

notes:

6.5 = 13/2

42.25 = 169/4

======================================================

Explanation:

The coefficient in front of the m is -13. Cut this in half to get -13/2 = -6.5

Then square this result to get (-6.5)^2 = 42.25

We need to add 42.25 to the expression in order to complete the square

This allows us to factor to get m^2 - 13m + 42.25 = (m - 6.5)^2

Note how the equation is in the form

a^2 - 2ab + b^2 = (a-b)^2

where a = m and b = 6.5

ill give brainliest to whoever helps

Answers

Answer:

25

Step-by-step explanation:

I think it’s 25 cause I did

[tex]x+30+x+40+2x+10=180[/tex]

[tex]4x+80=180[/tex]

[tex]4x=180-80[/tex]

[tex]\frac{4x}{4} =\frac{100}{4}[/tex]

[tex]x=25[/tex]

(b)

[tex]2(25)+10[/tex]

[tex]=50+10[/tex]

[tex]=60[/tex]

22. A) 25
X+30+X+40+2X+10=
4X+80=180
-80. -80
4X=100
4X/4= 100/4
X=25

B) 2(25)+10=60

help me with this and I will give you a chicken ​

Answers

Answer:

Mode:15

Mean:149

The Range:4

hope this helps don’t be mad if this is wrong pls don’t be mad if it’s wrong if it’s right hope it helps

SOMEONE PLEASE HELP ME ASAP THIS IS ALMOST DUE!!


The price of an iphone was reduced from $960 to $840. By what percentage was the price of the iphone reduced?

A. 13.5%
B. 12.2%
C. 13%
D. 12%

Answers

Answer:

13.5%

Step-by-step explanation:

I hope this helps and also searched the internet for the answer

Answer:

12.5%

Step-by-step explanation:

960-840=120

120/960=12.5%

4+4=? Trick Question :3

Answers

Answer:

8

Step-by-step explanation:

Lol hope this helps!

hmmmmm....... 10? :)

What is 6 x 1 1\4 in fractions

Answers

3/2 i’m pretty sure. apologies if i’m wrong

giving out brainliest answer please help me out asap !! it’s due today

Answers

Answer:

180=3x+7x+10

simplify

180=10x+10

subtract 10 from both sides

170=10x

divide both sides by 10

x=17

Put the steps in correct order to prove that if x is irrational, then 1/x is irrational using contraposition.

a. Substitute 1/x = p/q, to obtain x = 1/(1/x) = 1/(p/q) = q/p.
b. Hence x is rational.
c. If 1/x is rational, then 1/x = p/q for some integers p and q with q ≠ 0. Observe that p is not 0 either, because 1/x is not 0.
d. Observe that x is the quotient of two integers with the denominator nonzero.

Answers

Answer:

The correct order is:

a

c

d

b

Step-by-step explanation:

First, let's write 1/x in a convenient way for us:

a) Substitute 1/x = p/q, to obtain x = 1/(1/x) = 1/(p/q) = q/p.

Now we assume that 1/x is rational (we want to prove that this implies that x will be also rational and because we know that x is irrational assuming that 1/x is rational will lead to an incongruence), then:

c. If 1/x is rational, then 1/x = p/q for some integers p and q with q ≠ 0. Observe that p is not 0 either, because 1/x is not 0.

Now we know that we can write x as a quotient of two integers, we need to imply that, then the next one is:

d) Observe that x is the quotient of two integers with the denominator nonzero.

And that is the definition of rational, then we end with:

b) Hence x is rational.

Which is what we wanted to get.

One-way ANOVA and two-way ANOVA are different because:__________

a. The single factor in one-way ANOVA has only one level.
b. Each factor in the two-way ANOVA has exactly two levels.
c. The one-way ANOVA concerns a single factor with multiple levels and the two ANOVA concerns two factors with also multiple levels.
d. The one-way ANOVA concerns a single factor with a single level and the two ANOVA concerns two factors with a single level each.

Answers

Answer:

c. The one-way ANOVA concerns a single factor with multiple levels and the two ANOVA concerns two factors with also multiple levels.

Step-by-step explanation:

The main difference between one way anova and two way anova is that one way anova has a single independent variable and two way anova has two independent variables.

The dependent variables may vary . They may be one , two or three. They do not affect the method used.

So  one-way ANOVA concerns a single factor and  the two ANOVA concerns two factors.

So the best choice is option c.

2x(27x+5) Evaluate this please

Answers

Answer:

54x^2 + 10x

Step-by-step explanation:

Solve for X. What does X equal?

Answers

Step-by-step explanation:

Apply angle sum of triangle, that means the sum of all interior angles in a triangle is equal to 180°.

So that, (x + 45) + 50° + 90° = 180°.

However when we simply do 45+50+90, the answer is already bigger than 180.

So the question is made wrong.

If you’re solving the equation for X then X = -5

How much does 9.45 kg equal grams

Answers

Answer:

9.45 kg is 9450 grams.

Step-by-step explanation:

1 kg = 1000

9.45 x 1000 = 9450

Step-by-step explanation:

1kg =1000gram

9.45kg =9.45×1000

9450gram

hope it helps.

Can someone help me with question 1 and 2 please​

Answers

question 1)
there’s 180 degrees in a triangle
70 + 70 = 140
180 - 140= 40
A= 40
question 2)
there’s only one line of symmetry, down the middle

A picture frame measures 5 inches wide and 7 inches long. What is the perimeter of the frame?

Answers

The perimeter is 24.
Remember finding perimeter is always adding, so add 5 two times for the sides do the shape, do the same for 7, then you get your answer. Hope this helps!
the answer would be 24, 5+5+7+7=24

Please help what’s this answer ?! And the last answer is 2/5

Answers

Answer:

F  0.45

Step-by-step explanation:

Total number of students: 15 + 8 + 27 + 10 = 60

Number of students who took theater: 27

part = 27/60 = 0.45 = 45%

Answer: F   0.45

Answer:

I'm answering for your last question....it wouldn't let me post under the one that I had to

anyways your answer is d

Find the exact value of sin (13pi/8)

Answers

Answer:

degree 0.089

radian -0.92

Step-by-step explanation:

A rectangle measures 8 3 inches by 9 4 inches. What is its area?

Answers

Answer:

Step-by-step explanation:

7,802 in

What happens to y as x approaches negative infinity in the function y=log(x)

Answers

Answer:

There are no real values of y for  negative x,  for the function y = log(x).

Step-by-step explanation:

Need help asap! Please and thank you

Answers

Answer:

Choice A

Step-by-step explanation:

f(x) - g(x)

x^3 - 4x + 2 - (x - 2)^2

x^3 - 4x + 2 - (x^2 - 2x - 2x + 4)

x^3 - 4x + 2 - (x^2 - 4x + 4)

x^3 - 4x + 2 - x^2 + 4x - 4

x^3 - x^2 - 2

helppp please no links i give brainly-est just help UwU

Answers

Answer:

igure it out based on the explanation

Step-by-step explanation:

do left to right first do the divishon on the left get and answer divide that by 8 then divide the answer by 2 then subtract it by 3!

Answer only if you know if you put links I will report

Answers

Answer:

WHATS THE QUESTION, BRO??

Step-by-step explanation:

Nth term for quaratic sequence -7,-6,-3,2,9,18,29

Answers

Answer:

-7, -6, -3, 2, 9, 18, 29, 42, 57

Rule: + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17......................

1. What is the absolute value of 8?

Answers

Answer:

8

Step-by-step explanation:

Answer: 8

Step-by-step explanation: For absolute values, all values are positive. It is basically the positive inverse of the number.

What do you mutiply when doing surface area

Answers

Answer:

Depends on the shape for rectangles its base × height for triangles its base × height × 1/2

Which expression is equivalent to (see the picture)

A. 20x-21y +14
B. 20x + 11y + 14
C. 20x - 11y + 6
D. 20x + 21y +6

Answers

Answer:

A

Step-by-step explanation:

[tex]\frac{1}{5} (150x-80y+50-50x-25y+20)[/tex]

step 1 apply the 1/5 to everything that inside of the parenthesis

[tex]\frac{150x}{5} =30x\\\\\frac{-80y}{5} =-16y\\\\\frac{50}{5} =10\\\\\frac{-50x}{5} =-10x\\\\\frac{-25y}{5} =-5y\\\\\frac{20}{5} =4[/tex]

we now have 30x - 16y + 10 - 10x - 5y + 4

Step 2 combine like terms

30x - 10x = 20x

-16y - 5y = - 21y

10 + 4 = 14

we're left with 20x - 21y + 14 Which corresponds with answer choice A

Answer:

20x-21y+14

Step-by-step explanation:

1/5(150x-80y+50-50x-25y+20) is equal to 1/5(150x) + 1/5(-80y) + 1/5(50) + 1/5 (-50x) + 1/5(-25y) + 1/5(20)

So if we simplify, we would have 30x + (-16y) + 10 + (-10x) + (-5y) + 4, or 30x -16y + 10 -10x -5y + 4

When organizing the values by variable, the equation would look like this -

30x - 10x -16y -5y + 10 + 4

Combining like terms will result in 20x -21y + 14.

Hope this helps!

what happen when their is decrease in equilibrium price and increase in equilibrium quantity​

Answers

Answer: An increase in demand, all other things unchanged, will cause the equilibrium price to rise; quantity supplied will increase. A decrease in demand will cause the equilibrium price to fall; quantity supplied will decrease. ... A decrease in supply will cause the equilibrium price to rise; quantity demanded will decrease.

1. devin is making a candle by pouring melted wax into a mold in the shape of a square pyramid. each side of the base of the pyramid is 6 cm and the height of the pyramid is 9 cm. to get the wax for the candle, devin melts cubes of wax that are each 4 cm by 4 cm by 4 cm. how many of the wax cubes will devin need in order to make the candle? show your work.

Answers

Answer:

1.6875

Step-by-step explanation:

Volume of a pyramid = 1/3 (l*w*h)

Volume = 1/3(6 * 6 * 9)

Volume = 2 * 6 * 9

Volume = 108 cm³

Volume of cube = s³ ; s = side length

Volume = 4³ = 4 * 4 * 4 = 64 cm³

Number of wax cube = Volume of pyramid / volume of cube

= 108 cm³ / 64 cm³

= 1.6875

The ratio of red jelly beans to green jelly beans in a jar is 5:4. If there are 108 total jelly beans in the jar then how many red jelly beans must be in the jar?

Answers

Answer:

21

Step-by-step explanation:

5.
13 points
A piece of jewelry that regularly costs $120 is on sale for $96. What is the percent of decrease in the
price of the jewelry piece?
A 15%
B 20%
C 18%
D 30%

Answers

Answer:

The answer is B

Step-by-step explanation:

The answer would be B....

There are 39,945 people in a baseball stadium.
4,130 are rooting for the away team, and the rest
are rooting for the home team. Enter the number
of people who are rooting for the home team.

Answers

Answer:

35815

Step-by-step explanation:

just subtract

Answer:

35,815 people rooted for the home team.

Step-by-step explanation:

Subtract the total people watching by the people rooting for the away team.

39,945 - 4,130 = 35,815

Hope this helps! :)

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