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Hitman42 [59]
3 years ago
6

Suppose after 2500 years an initial amount of 1000 grams of a radioactive substance has decayed to 75 grams. What is the half-li

fe of the substance? The half-life is:_______.
(A) Less than 600 years
(B) Between 600 and 700 years
(C) Between 700 and 800 years
(D) Between 800 and 900 years
(E) More than 900 years
Mathematics
1 answer:
krok68 [10]3 years ago
5 0

Answer:

The correct answer is:

Between 600 and 700 years (B)

Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years

First, let us calculate the decay constant (k)

75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036

Next, let us calculate the half-life as follows:

\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2}  \approx 669\ years

Therefore the half-life is between 600 and 700 years

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Consider each of the following relationships. Which school shows the greatest rate of change between male and female students?
ratelena [41]

Answer:

The school C shows the greatest rate of change between male and female students

Step-by-step explanation:

Let

x -----> the number of female students

y ----> the number of male students

we know that

The ratio of male students to female students is

\frac{y}{x}

we have

<em>School A</em>

\frac{y}{x}=\frac{4}{1}=4

<em>School B</em>

\frac{y}{x}=\frac{4}{3}=1.33 ----> the slope of the linear equation

<em>School C</em>

\frac{y}{x}=\frac{1,260}{280}=4.5

so

4.5 > 4 > 1.33

therefore

The school C shows the greatest rate of change between male and female students

7 0
3 years ago
Miss Perkins buys 1.8 lbs of ground beef to make tacos
bixtya [17]
It will cost her $8.55 at $4.75 a pound
7 0
3 years ago
Keelin’s hourly rate went from $9.50 per hour to $10.25 per hour. What is the percent increase?
bazaltina [42]

Answer:

.75 would be your answer to your question!

I hope this really answered your question and i'm really happy to help!

Step-by-step explanation:

So you would take the $9.50 + .75 and you will get the answer $10.25

3 0
3 years ago
After a 75% reduction, you purchase a new DVD player on sale for $136. What was the original price of the DVD player
iogann1982 [59]

Answer:

$544

Step-by-step explanation:

To determine the original price of the DVD player considering that you know that it had a 75% reduction, you can use a rule of three as the price of $136 represents 25% of the original price and with this you can calculate the price that represents 100%:

$136 → 25%

  x    ← 100%

x=(136*100)/25=$544

According to this, the answer is that the original price of the DVD player was $544.

8 0
3 years ago
For each of these relations on the set {21, 22, 23, 24}, decide whether it is reflexive, whether it is symmetric, whether it is
bonufazy [111]

Answer:

Step-by-step explanation:

I. { (22,22) , (22,23) , (22,24) , (23,22) , (23,23) , (23,24) }

Reflexive : True because we see the pairs (22,22) , (23,23)..

Symmetrix : NO, as we see the pairs (22,24) BUT NOT (24,22)

Transitive : YES, As we see (22,22 ) and (22, 24) , we see the pairs (22,24)

Antisymmetric : NO

II){ (21,21) , (21,22) , (22,21) , (22,22) , (23,23) , (24,24) }

Reflexive : True because we see the pairs (22,22) , (23,23) (21,21)

Symmetrix : Yes, as we see the pairs (21,22) AND (22,21)

Transitive : YES,

Antisymmetric : NO

7 0
3 years ago
Read 2 more answers
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