1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alexandr402 [8]
3 years ago
12

The ​half-life of a radioactive element is 130​ days, but your sample will not be useful to you after​ 80% of the radioactive nu

clei originally present have disintegrated. About how many days can you use the​ sample? Round to the nearest day.
Mathematics
1 answer:
gtnhenbr [62]3 years ago
7 0

Answer:

We can use the sample about 42 days.

Step-by-step explanation:

Decay Equation:

\frac{dN}{dt}\propto -N

\Rightarrow \frac{dN}{dt} =-\lambda N

\Rightarrow \frac{dN}{N} =-\lambda dt

Integrating both sides

\int \frac{dN}{N} =\int\lambda dt

\Rightarrow ln|N|=-\lambda t+c

When t=0, N=N_0 = initial amount

\Rightarrow ln|N_0|=-\lambda .0+c

\Rightarrow c= ln|N_0|

\therefore ln|N|=-\lambda t+ln|N_0|

\Rightarrow ln|N|-ln|N_0|=-\lambda t

\Rightarrow ln|\frac{N}{N_0}|=-\lambda t.......(1)

                            \frac{N}{N_0}=e^{-\lambda t}.........(2)

Logarithm:

  • ln|\frac mn|= ln|m|-ln|n|
  • ln|ab|=ln|a|+ln|b|
  • ln|e^a|=a
  • ln|a|=b \Rightarrow a=e^b
  • ln|1|=0

130 days is the half-life of the given radioactive element.

For half life,

N=\frac12 N_0,  t=t_\frac12=130 days.

we plug all values in equation (1)

ln|\frac{\frac12N_0}{N_0}|=-\lambda \times 130

\rightarrow ln|\frac{\frac12}{1}|=-\lambda \times 130

\rightarrow ln|1|-ln|2|-ln|1|=-\lambda \times 130

\rightarrow -ln|2|=-\lambda \times 130

\rightarrow \lambda= \frac{-ln|2|}{-130}

\rightarrow \lambda= \frac{ln|2|}{130}

We need to find the time when the sample remains 80% of its original.

N=\frac{80}{100}N_0

\therefore ln|{\frac{\frac {80}{100}N_0}{N_0}|=-\frac{ln2}{130}t

\Rightarrow ln|{{\frac {80}{100}|=-\frac{ln2}{130}t

\Rightarrow ln|{{ {80}|-ln|{100}|=-\frac{ln2}{130}t

\Rightarrow t=\frac{ln|80|-ln|100|}{-\frac{ln|2|}{130}}

\Rightarrow t=\frac{(ln|80|-ln|100|)\times 130}{-{ln|2|}}

\Rightarrow t\approx 42

We can use the sample about 42 days.

You might be interested in
Find the rule, solve for n
Andrej [43]
Try this option:
note, that the difference between 8 and 10 is 2, between 9 and 12 is 3, between 11 and 16 is 5. It is possible when f(x) is linear function, 2x-6, therefore f(14)=2*14-6=22

Answer: 22.
6 0
3 years ago
The inequality for the graph and please answer quickly
Marizza181 [45]

Answer:

x ≥ 1

Step-by-step explanation:

  1. The circle is over 1
  2. The circle is closed (filled in), which means it will be either ≤ or ≥.
  3. The arrow is pointing right, so it's ≥.
  4. The number can be represented by x
  5. Put it together: x ≥ 1

I hope this helps!

3 0
3 years ago
After I substitute in y how do I determine the coordinate(s)?
klasskru [66]
Simplifying both sides of the equation then isolating the variable
6 0
3 years ago
A teacher writes the name of each of her 25 students on a slip of paper and places the papers in a box. To call on a student, sh
Gre4nikov [31]

Answer:

0.56

Step-by-step explanation:

There are 14 girls, and a total of 25 students.  So the probability of selecting a girl is P = 14/25 = 0.56.

8 0
3 years ago
Read 2 more answers
All of the equations to –32 = k + –19
soldi70 [24.7K]

Answer:

k =  - 13

Step-by-step explanation:

- 32 = k - 19 \\  -32 + 19 =  k \\  - 13 = k

8 0
2 years ago
Other questions:
  • 1/3 divide by 3/8 =?
    5·1 answer
  • A constant force F=47i+30j moves an object along a vector D=13i-8j. find the work done
    6·2 answers
  • At olivers pizza palace in the six hours they were open they sold the fowling number of pizzas: 55 pepperoni 57 sausage 50 chees
    10·1 answer
  • You measure the sides of a pool and find that it is 20 yards wide and 60 yards long.
    7·2 answers
  • PLEASE HELP!!!
    14·2 answers
  • Mika paints the neighbors fence the cost of the paint was 96$ the neighbor paid Mika 15$ per hour create the equation that can b
    8·1 answer
  • Please show me how to COMPLETELY factor this expression.
    9·1 answer
  • Find the arc length, x, when<br> ,<br> r= 1 and 8 = 2.5 radians.<br> Х<br> 2.5<br> 1<br> x = [?]
    15·1 answer
  • I WILL GIVE BRAINLIEST
    7·1 answer
  • HELPEHEGEDHGDGXCCVCCXVV
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!