Pleaseeee someone help me . What is the half life of Caron 14 of this problem ???

Answer:

5730 years

Explanation:

In a chemical reaction, including radioactive decay, the half-life of a species is the time taken for the substance to decrease to exactly one-half its initial value.

For a first-order reaction, the half-life of the reactant is

                                                  [tex]t_{\frac{1}{2}} \ = \ \displaystyle\frac{\ln 2}{\lambda} \ \ \ \ \ \ (1)[/tex],

where λ is the reaction's rate constant modeled by the differential equation describing the kinetics of a first-order reaction

                                               [tex]N \ = \ N_{0}e^{-\lambda t} \ \ \ \ \ (2)[/tex],

where N is the remaining amount of substance after time t and [tex]N_{0}[/tex] is the initial amount of substance before the chemical reaction proceeds.

Since the value of λ is constant, rearrange equation (1) with λ as the subject,

                                                       [tex]\lambda \ = \ \displaystyle\frac{\ln 2}{t_{\frac{1}{2}}}[/tex].

Given that only 12.5% of carbon-14 remained after 17190 years assuming that initially there was 100% of carbon -14, substitute in the values into equation (2) and solve for λ (make λ the subject of the equation),

                               [tex]\-\hspace{0.56cm}12.5 \ = \ 100e^{-\lambda \times 17190} \\ \\ \-\hspace{0.5cm} \displaystyle\frac{12.5}{100} \ = \ e^{-17190\lambda} \\ \\ \displaystyle\frac{\ln\displaystyle(\frac{1}{8})}{-17190} \ = \ \lambda \\ \\ \-\hspace{1.05cm} \lambda \ = \ \displaystyle\frac{3\ln2}{17910} \ \ \ \ \ \ \ \ \ \ (\ln \displaystyle\frac{1}{x} \ = \ -\ln x\ ; \ \ln x^{n} \ = \ n\ln x )[/tex]

Equate both λ,

                                            [tex]\displaystyle\frac{\ln 2}{t_{\frac{1}{2}}} \ = \ \displaystyle\frac{3\ln2}{17190} \\ \\ \-\hspace{0.26cm} t_{\frac{1}{2}} \ = \ \ln 2 \ \times \ \displaystyle\frac{17190}{3\ln2} \\ \\ \-\hspace{0.26cm} t_{\frac{1}{2}} \ = \ \displaystyle\frac{17190}{3} \\ \\ \-\hspace{0.26cm} t_{\frac{1}{2}} \ = \ 5730[/tex]

*Note that the above calculations demonstrated that carbon-14 went through 3 half-lives to yield a remaining 12.5% of its original amount, since

                                 [tex]100\% \ \overset{t_{\frac{1}{2}}}\longrightarrow \ 50\% \ \overset{t_{\frac{1}{2}}}\longrightarrow \ 25\% \overset{t_{\frac{1}{2}}}\longrightarrow \ 12.5\%[/tex].

Therefore, if n is the time taken for carbon-14 to half its initial amount trice to remain 12.5% of its initial amount. Then, the half-life of carbon-14 is [tex]\displaystyle\frac{n}{3}[/tex].

Many livestock are being grazed on public lands because the fees to graze on public lands are cheaper than the fees for private lands. If we aren't careful, what can this cause? A. owners moving their livestock TO private lands B. increased fees for private lands C. overgrazing on public lands D. overgrazing on private lands​

a. Viruses reproduce using a ______ _____.



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c.hormones
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B) random motion from one part of a membrane to another, from a lower concentration to a higher concentration.

C) straight line motion from one part of a membrane to another, from a higher concentration to a lower concentration.

D) straight line motion from one part of a membrane to another, from a lower concentration to a higher concentration.

Answer:
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15. Stephanie made the following chart for the terrestrial planets. What correction needs to be made?
Mercury
Venus
Earth
Mars
no atmosphere
very thick atmosphere
medium atmosphere
no atmosphere
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2nd planet
3rd planet
4th planet
1 year is shorter than Earth's year.
1 year is short than Earth's year.
1 year is approximately 365 days.
1 year is longer than Earth's year.
O Mars's year is shorter than Earth's year.
O Mercury's year is longer than Earth's year.
A
O Mars has a thin atmosphere
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down
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2. means that hydrogen has been added to unsaturated fats
4 a large molecule whose main function is energy storage
6. unsaturated fats have move _____ bonds than saturated

UP
3. lipids are water-avoiding or _____
5. female and male hormones are example of ____
7. animal fats are said to be ____
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B) The advantage of the mutations is dependent on the environment and external conditions.

C) While mutations provide genetic variation they did not play a role in natural selection.

D) The speckled mutation provided an advantage while the black mutation was a disadvantage for survival.

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Generation 1 Generation 2 Generation 3
Tusks greater than 2.5 m in length 25 25 25
Tusks less than 2.5 m in length 75 75 75
Mass greater than 4,000 kg 15 15 15
Mass less than 4,000 kg 85 85 85
Fur thickness greater than 6 cm 15 25 35
Fur thickness less than 6 cm 85 75 65
Based on this data and your knowledge of natural selection, which explanation best explains the trends seen in the data?

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B.Individuals within this population of mammoths tend to only mate with individuals that have thick fur.
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D.Individuals with thick fur migrated into the population of mammoths, increasing the proportion of these individuals.

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plants and animals
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