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
Hitman42 [59]
2 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]2 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

You might be interested in
Can anyone help me plz​
Kryger [21]

Answer:Ok

You need to get x by itself.

8x + c = k

Subtract c.

8x = k - c

Divide 8 from both sides.

x = k - c / 8

So, I believe it is D

Step-by-step explanation:

4 0
3 years ago
Angie and Kenny play online video games. Angie buys 1 software package and 1 month of game play. Kenny buys 1 software package a
balandron [24]

The cost of one month of game play is $14

Step-by-step explanation:

Angie and Kenny play online video games

  • Angie buys 1 software package and 1 month of game play
  • Kenny buys 1 software package and 3 months of game play
  • Each software package costs ​$20
  • If their total cost is ​$96

We need to find the cost of one month of game play

∵ Angie buys 1 software package

∵ Kenny buys 1 software package

∵ Each software package costs ​$20

- Find the total cost of their software package

∴ The total cost of their software package = 20 × 1 + 20 × 1

∴ The total cost of their software package = 20 + 20 = 40

∴ The total cost of their software package is $40

Assume that the cost of one month of game​ play is $x

∵ The cost of one month of game​ play = x

∵ Angie buys 1 month of game play

∵ Kenny buys 3 months of game play

- Find the total cost of their game​ play

∴ The total cost of their game play = x × 1 + x × 3

∴ The total cost of their game play = x + 3x = 4x

∴ The total cost of their game play is $4x

∵ Their total cost is ​$96

- Add the costs of their software package and their game

   play and equate the sum by 96

∴ 40 + 4x = 96

- Subtract 40 from both sides

∴ 4x = 56

- Divide both sides by 4

∴ x = 14

The cost of one month of game play is $14

Learn more:

You can learn more about the word problems in brainly.com/question/10557938

#LearnwithBrainly

4 0
3 years ago
send help!!!! Please!! The sum of the measures of the angles from any triangle is 180 degrees. In triangle ABC, angles A and B h
Ratling [72]

Let Angle A = X

Since Angle B is the same, angle B is also X

Then angle C = X +45


Add the 3 angles together: X +X +X +45 = 3x+45


That equals 180 degrees:

3x+45 = 180

Subtract 45 from both sides:

3x = 135

Divide both sides by 3:

X = 135/3

X = 45

Angle A = 45

Angle B = 45

Angle C = 45+45 = 90

7 0
3 years ago
Complete the table of values for this absolute value function. Then use the drawing tool(s) to graph the function. F(x)-2|x+1|-1
rusak2 [61]

Answer:

Please check the explanation!

Step-by-step explanation:

Given the equation

f\left(x\right)=-2|x+1|-1

As some of the absolute rules are:

  • \left|a\right|=a,\:a\ge 0
  • \:|-a|=a,\:\quad \:a>0

NOW, let us solve!

Let us substitute all the table values

Putting x = -4

y=-2\left|-4+1\right|-1        ∵\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0

y=-6-1

y=-7

So, when x = -4, then y = -7

Putting x = -3

y=-2|-3+1|-1\:

y=-4-1

y=-5

when x = -3, then y = -5

Putting x = -2

y=-2\left|-2+1\right|-1

y=-2-1

y=-3

when x = -2, then y = -3

Putting x = -1

y=-2\left|-1+1\right|-1

y=-0-1

y=-1

when x = -1, then y = -1

Putting x = 0

y=-2\left|0+1\right|-1

y=-2-1

y=-3

when x = 0, then y = -3

Putting x = 1

y=-2\left|1+1\right|-1

y=-4-1

y=-5

when x = 1, then y = -5

The graph is also attached below.

6 0
3 years ago
Could someone give me the answers do these please
Debora [2.8K]
5. (0,1)
6. (-2,-2)
7. (-1,-3)
8. (-3, 2)
5 0
3 years ago
Read 2 more answers
Other questions:
  • M is the midpoint of AB, M is (7,2) and A is (6,7), what is the coordinate of B
    8·1 answer
  • For the expression 6 − y + 3, determine the coefficient for the variable term. (2 points) −1 0 3 6
    11·2 answers
  • A yogurt shop offers two different flavors of frozen yogurt (chocolate and vanilla) and three different toppings (sprinkles, cho
    11·1 answer
  • A delivery truck traveled ¼ of its route in 2 hours How long does it take to complete one route?
    6·2 answers
  • Need help please (: Show how to apply the order of operation rules as you simplify the following expression
    14·1 answer
  • I’m hella confused????
    9·1 answer
  • Please help it’s for a test it’s due in 30 minutes!!!!!!!
    6·1 answer
  • Please help a girl out!! really confused
    10·1 answer
  • A washer and a dryer cost $562 combined. The washer costs $88 less than the dryer. What is the cost of the dryer?
    13·2 answers
  • Website: Mathswatch <br> #Problem solving
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!