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3 years ago

8

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate

parameter of 2.4% per hour. How many hours does it take for the size of the sample to double?

1 answer:

sveta [45]3 years ago

6 0

Answer:

It would take approximately 289 hours for the population to double

Explanation:

Recall the expression for the continuous exponential growth of a population:

$N(t)=N_0\,e^{kt}$

where N(t) measures the number of individuals, No is the original population, "k" is the percent rate of growth, and "t" is the time elapsed.

In our case, we don't know No (original population, but know that we want it to double in a certain elapsed "t". We also have in mind that the percent rate "k" would be expressed in mathematical form as: 0.0024 (mathematical form of the given percent growth rate).

So we need to solve for "t" in the following equation:

$2\,N_0=N_0\,e^{0.0024\,t}\\\frac{2\,N_0}{N_0} =e^{0.0024\,t}\\2=e^{0.0024\,t}\\ln(2)=0.0024\,t\\t=\frac{ln(2)}{0.0024} \\t=288.811\,\, hours$

Which can be rounded to about 289 hours

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A 7.00-g bullet, when fired from a gun into a 1.00-kg block of wood held in a vise, penetrates the block to a depth of 8.00 cm.

gulaghasi [49]

Answer:

In the second case there's no way to know what depth the bullet will penetrate into the block.

Explanation:

Since the block is on a <em>frictionless </em>surface, when hitted by the bullet, this last one could barely penetrate the surface of the block and, both, start moving as one (<em>perfectly inellastic collition</em>) since here, there's no vise to hold the block into place.

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3 years ago

How many coulombs of positive charge are there in 3.60 kg of plutonium, given its atomic mass is 244 and that each plutonium ato

PtichkaEL [24]

1 mole of plutonium = 244 gm

3.6 kg of plutonium = 3.6 × 1000 = 3600 gm

Number of moles = 3600 ÷ 244 = 14.754 moles

One moles of plutonium contains protons = $6.023 \times {10}^{23} \times 94$

Total number of protons in 14.754 moles = $6.023 \times {10}^{23} \times 94 \times 14.754$

Total number of protons in 14.754 moles = $8353.15 \times {10}^{23}$

Total Positive charge = $8353.15 \times {10}^{23} \times 1.6 \times {10}^{-19}$

Total positive charge = $13365.04 \times {10}^{4}$ C

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3 years ago

In atoms, electrons surround the nucleus in

nasty-shy [4]

In atoms, electrons surround the nucleus in specific energy levels.

Answer: Option B

<u>Explanation: </u>

Atom, actually considered as the tiny part that is ever present in this universe. Many theories and experiments were conducted, for studying what was present inside of an atom, and many theories came into light.

And finally, Bohr-Sommerfeld Theory stated the final conclusion, that the positive charge is at the centre of the nucleus, and all the electrons revolve in their specific energy levels. If an atom wants to move to lower energy state, it should emit energy, whereas for going to higher state, it should gain energy.

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3 years ago

Suppose that you are swimming in a river while a friend watches from the shore. In calm water, you swim at a speed of 1.25 m/s .

aliya0001 [1]

Answer: The observing friend will the swimmer moving at a speed of 0.25 m/s.

Explanation:

Let <em>S</em> be the speed of the swimmer, given as 1.25 m/s

Let $S_{0}$ be the speed of the river's current given as 1.00 m/s.

Note that this speed is the magnitude of the velocity which is a vector quantity.

The direction of the swimmer is upstream.

Hence the resultant velocity is given as, $S_{R}$ = S — S 0 $S_{0}$

$S_{R}$ = 1.25 — 1

$S_{R}$ = 0.25 m/s.

Therefore, the observing friend will see the swimmer moving at a speed of 0.25 m/s due to resistance produced by the current of the river.

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3 years ago

A janitor standing on the top floor of a building wishes to determine the depth of the elevator shaft. They drop a rock from res

Bumek [7]

Answer:

Part a)

H = 26.8 m

Part b)

error = 7.18 %

Explanation:

Part a)

As the stone is dropped from height H then time taken by it to hit the floor is given as

$t_1 = \sqrt{\frac{2H}{g}}$

now the sound will come back to the observer in the time

$t_2 = \frac{H}{v}$

so we will have

$t_1 + t_2 = 2.42$

$\sqrt{\frac{2H}{g}} + \frac{H}{v} = 2.42$

so we have

$\sqrt{\frac{2H}{9.81}} + \frac{H}{336} = 2.42$

solve above equation for H

$H = 26.8 m$

Part b)

If sound reflection part is ignored then in that case

$H = \frac{1}{2}gt^2$

$H = \frac{1}{2}(9.81)(2.42^2)$

$H = 28.7 m$

so here percentage error in height calculation is given as

$percentage = \frac{28.7 - 26.8}{26.8} \times 100$

$percentage = 7.18$

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3 years ago