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densk [106]
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?
Physics
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 block of mass m=16.8 kg is sliding on a surface with initial velocity v=23.2 m/s. The block has a coefficient of kinetic frict
Firdavs [7]

Answer:

t = 23.92 s

Explanation:

Newton's second law:

∑F = m*a Formula (1)

∑F : algebraic sum of the forces in Newton (N)

m : mass s (kg)

a : acceleration  (m/s²)

We define the x-axis in the direction parallel to the movement of the block  and the y-axis in the direction perpendicular to it.

Forces acting on the block

W: Weight of the block : In vertical direction, downward

FN : Normal force : perpendicular to the floor, upward

fk :  Kinetic friction force: parallel to the floor  and opposite to the movement

F = 86.4 N , in the direction of the motion

Calculated of the W

W= m*g

W=  16.8 kg* 9.8 m/s² = 164.64 N

Calculated of the FN  

We apply the formula (1)  

∑Fy = m*ay ay = 0  

FN - W = 0  

FN = W  

FN =  164.64 N

Calculated of the fk

fk  = μk*FN

fk  = 0.426* 164.64 N

fk  = 70.13 N

We apply the formula (1) to calculated acceleration of the block:

∑Fx = m*ax  ,  ax= a  : acceleration of the block

F - fk = m*a

86.4 -70.13  = (16.8)*(-a)

16.26 =  (16.8)*(-a)

a = -(16.26 )/ (16.8)

a = - 0.97 m/s²

Kinematics of the block

Because the block moves with uniformly accelerated movement we apply the following formula :

vf = v₀ + a*t   Formula (2)

Where:  

t: time interval  (m)

v₀: initial speed  (m/s)

vf: final speed   (m/s)

Data:

v₀ = 23.2 m/s

vf = 0

a =  -0.97 m/s²  

Time it takes for the block to stop

We replace data in the formula (2)  to calculate the time

vf= v₀+a*t

0 = 23.2+( -0.97)*t

(0.97)*t  = 23.2

(0.97)*t  = 23.2

t = 23.2 / (0.97)

t = 23.92 s

7 0
3 years ago
What is the energy of light that must be absorbed by a hydrogen atom to transition an electron from n = 3 to n = 5?
alina1380 [7]

Answer:

The energy absorbed by a hydrogen atom is 1.549 X10⁻¹⁹ J

Explanation:

Using Bohr's equation; the energy absorbed by the hydrogen atom can be calculated as follows:

\delta E = (\frac{1}{n_2{^2}} -\frac{1}{n_1^{2}})13.6eV

When an electron moves from a lower energy level to a higher energy level, energy is absorbed by the atom.

Lower energy level (n₂) = 3

Higher energy level (n₁) = 5

1 eV = 1.602X10⁻¹⁹ C

\delta E = (\frac{1}{3{^2}} -\frac{1}{5^{2}})13.6X1.602X10^{-19}

ΔE = 1.549 X10⁻¹⁹J

The energy absorbed by a hydrogen atom  to transition an electron from n = 3 to n = 5 is 1.549 X10⁻¹⁹ J

4 0
3 years ago
A box sits on a table. A short arrow labeled F subscript N points up. A short arrow labeled F subscript g points down. A long ar
Aloiza [94]

Answer:

unbalanced and right

Explanation:

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3 years ago
If 100 grams of vinegar and 5 grams of baking soda are poured in a container, a small amount of gas will be produced. What will
Anit [1.1K]
It will be a little bit less because of evaporation i learned that in third grade and your in high school that is sad
5 0
3 years ago
In which situation is work not being done?
almond37 [142]

AS

work done =W = F.d = F d cosФ     (Ф is angle between force F and displacement d) If a body/object is moving on a smooth surface (friction-less surface ) .There is no force acting on that body.  F=0 so W=FdcosФ= (0)dcosФ ⇒ W=0

Now if a body is facing some amount of force but under the action of force there is no displacement covered. d=0 so W =FdcosФ= F(0)cosФ ⇒W=0

example:  A person is applying a force on rigid wall but wall remains at rest there is no displacement occurs in wall.

The third term upon which work done  dependent is angle between force and displacement i.e Ф. If Ф=90° then W= FdcosФ= Fdcos90⇒ W=0   ( as cos 90°=0)

5 0
3 years ago
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