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]
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]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
-2 (z + 11) = 6<br><br> Please help. You have to use distributive property.
Mamont248 [21]

Answer:

-14

Step-by-step explanation:

-2(z+11)=6

-2z-22=6

-2z=28

z=-14

4 0
2 years ago
What is the approximate area of a sector of a circle with a radius of 8 cm, and a minor arc of 70 degrees?
oee [108]

Answer:

39.0953=39cm2

Step-by-step explanation:

Minor arc =70

Angle of arc=70

Then this sector =70/360=7/36 of the circle

Then area = 7/36x3.14x8x8=39cm2 approximatly

5 0
2 years ago
X over 3 equals 1 over 4. how do i solve this in algebra? its solving one-step equations.
Snezhnost [94]

Cross multiply  X×4=3×1 4x=3 X= 3/4

6 0
3 years ago
An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is
Dmitry_Shevchenko [17]
Fidn volume
V=hpir^2
d/2=r
1.4/2=0.7=r
height=3.5
V=3.5*3.14*0.7^2
V=5.3851

1.5 times t=5.3851
divide both sides by 1.5
t=3.59
round
t=4

4 minutes
6 0
3 years ago
For five mathematics tests, your scores were 81, 86, 81, 76, 71. what was your average score?
trasher [3.6K]

add them together then divide by 5

81 +86 +81 +76 +71 = 395

395/5 = 79

 your average was 79

7 0
3 years ago
Other questions:
  • What is the measure of ∠A, to the nearest degree?
    15·1 answer
  • What is the domain and range of y=1+1/x
    10·1 answer
  • Graph the linear equation y = - 2/3
    12·1 answer
  • A house cost $120,000 when it was purchased. The value of the house increases by 10% each year. Find the rate of growth each mon
    15·1 answer
  • What is -0.38,-3/8,-0.04 in order from least to greatest
    10·1 answer
  • What is 4(x+3) = 2(2x+9)<br> What is x
    8·1 answer
  • Which is the simplified form of the expression 3(7/6x + 4) - 2(3/2-5/4x)<br><br><br>​
    14·1 answer
  • Trevor Jackson wants to take out a loan in order to buy a house, so he gave the bank permission to check his credit report. Base
    9·1 answer
  • There are 60 pupils who joined the Math Quiz Competetion. 40 were boys and 20 were girls. During the Awarding ceremony, it was f
    7·1 answer
  • NEED ANWSERS 16-21 FAST
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!