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
Shkiper50 [21]
3 years ago
6

A sample of a radioactive substance decayed to 97% of its original amount after a year. (Round your answers to two decimal place

s.) (a) What is the half-life of the substance? 22.76 Correct: Your answer is correct. yr (b) How long would it take the sample to decay to 85% of its original amount? yr
Mathematics
1 answer:
Andrej [43]3 years ago
8 0

Answer:

a) The half life of the substance is 22.76 years.

b) 5.34 years for the sample to decay to 85% of its original amount

Step-by-step explanation:

The amount of the radioactive substance after t years is modeled by the following equation:

P(t) = P(0)(1-r)^{t}

In which P(0) is the initial amount and r is the decay rate.

A sample of a radioactive substance decayed to 97% of its original amount after a year.

This means that:

P(1) = 0.97P(0)

Then

P(t) = P(0)(1-r)^{t}

0.97P(0) = P(0)(1-r)^{0}

1 - r = 0.97

So

P(t) = P(0)(0.97t)^{t}

(a) What is the half-life of the substance?

This is t for which P(t) = 0.5P(0). So

P(t) = P(0)(0.97t)^{t}

0.5P(0) = P(0)(0.97t)^{t}

(0.97)^{t} = 0.5

\log{(0.97)^{t}} = \log{0.5}

t\log{0.97} = \log{0.5}

t = \frac{\log{0.5}}{\log{0.97}}

t = 22.76

The half life of the substance is 22.76 years.

(b) How long would it take the sample to decay to 85% of its original amount?

This is t for which P(t) = 0.85P(0). So

P(t) = P(0)(0.97t)^{t}

0.85P(0) = P(0)(0.97t)^{t}

(0.97)^{t} = 0.85

\log{(0.97)^{t}} = \log{0.85}

t\log{0.97} = \log{0.85}

t = \frac{\log{0.85}}{\log{0.97}}

t = 5.34

5.34 years for the sample to decay to 85% of its original amount

You might be interested in
Your friend uses the equation c=50p to find the total cost c for the number of people p internal local amusement park create a t
AnnZ [28]

We are given equation c=50p.

c is the total cost and p is the number of people.

Let us take number of people by groups of 10, 20, 30,40 people.

Note: We can take any positive integer for number of people in a group.

Now, we need to plug p=10, 20, 30,40 one by one in given function c=50p to find the costs c.

Plugging p=10, we get

c= 50*10 = 500.

Plugging p=20, we get

c= 50*20 = 1000.

Plugging p=30, we get

c= 50*30 = 1500.

Plugging p=40, we get

c= 50*40 = 2000.

So, we can create a table as.

Number of people (p)           Total cost (c)

--------------------------------------------------------------------

         10                                      500

         20                                     1000

         30                                     1500

         40                                     2000


4 0
3 years ago
Greta bought 3 lb and 4 oz of peanuts and shared 1 lb 12 oz with the class. what is the weight of the remaining peanuts ?
makkiz [27]

Answer:

1lb 8 oz

Step-by-step explanation:

Take 3 lbs and separate it into 48oz + 4 oz = 52 oz.

Same with the 1 lb 12 oz. 16 oz + 12 oz = 28.

Subtract 28 from 52 = 24 oz = 1 lb  8 oz.

Hope this helps.

5 0
3 years ago
Simplify the following expression:<br><br> 2(x+7) - (x+2)
Mekhanik [1.2K]

Answer:

x + 12

Step-by-step explanation:

  • (2)(x)+(2)(7) + (-1)(x) + (-1)(2)
  • 2x + 14 -x -2
  • (2x-x)+(14-2)
  • x + 12

Therefore, the answer is x + 12.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

8 0
2 years ago
Read 2 more answers
If 60 newspapers cost $27, find the cost of 16
Tju [1.3M]
16 newspapers cost $7.20
3 0
3 years ago
Jo says she can find the percent equivalent of 3/4 by multiplying the percentage equivalent of 1/4 by 3. How can you use a perce
schepotkina [342]
You can by filling 1 out of 4 bars then multiply the shaded bars by 3<span />
4 0
3 years ago
Other questions:
  • #7 Casey said that 40 people were surveyed. Is his answer reasonable? Explain
    10·2 answers
  • jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her
    7·2 answers
  • There are 50 sheets of drawing paper.
    8·1 answer
  • The solution of c+d&lt;−6 is c&lt;−8. What is the value of d?
    15·2 answers
  • Prove that lim x-&gt;0 cos(1/x) does not exist.
    12·1 answer
  • Can u pls help me with this question asap ​
    12·2 answers
  • Help me pleaseeee i’m begging!!!!
    15·1 answer
  • 2<br> What is (2 + 0.4 + 0.6)= ?
    11·1 answer
  • Pls help this is due in 15 minutes I’ll brainlest for the right answer
    10·2 answers
  • Write an expression that represents the weight of an object that weighs 12 pounds and increases by 0.5 pound per month. Let m be
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!