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
Expand and simplify <img src="https://tex.z-dn.net/?f=%20%283x-2%29%5E%7B2%7D%20" id="TexFormula1" title=" (3x-2)^{2} " alt=" (3
Rus_ich [418]
You can just 1) multiply the binomial by itself, or you can use 2) the square of a binomial pattern. I'll show it to you both ways.

1) Multiply the binomial by itself.

(3x - 2)^2 = (3x - 2)(3x - 2) =

Multiply every term of the first binomial by every term of the second binomial, then collect like terms. (This is often called using FOIL.)

= 9x^2 - 6x - 6x + 4

= 9x^2 - 12x + 4

2) Use the square of a binomial pattern

The square of a binomial is

(a - b)^2 = a^2 - 2ab - b^2

a^2 is the square of the first term.
b^2 is the square of the second term.
-2ab is the product of the two terms and 2.

You have

(3x - 2)^2,
where the first term is 3x, and the second term is -2

square the first term: 9x^2
square the last term: 4
the product of the terms and 2 is: -12x

Put it all together, and you get

9x^2 - 12x + 4

just like we got above with the other method.
7 0
3 years ago
Simplify the expression 3^-8× 34.
Alborosie

Answer:

= \frac{34}{6561}

Step-by-step explanation:

= 3^{-8}\times \:34\\= 34\times \frac{1}{3^{8} } \\= \frac{1\times \:34}{3^{8} } \\= \frac{34}{3^{8} } \\= \frac{34}{6561}

5 0
3 years ago
Identify the initial value and rate of change for the graph shown. (4 points)
spin [16.1K]

Answer:

a

Step-by-step explanation:

8 0
3 years ago
Someone anybody please help
babymother [125]
This is a system of equations problem that can be solved using one of three methods: <span>graphing, substitution, or <span>elimination. I'll be using substitution.

In substitution:
1) S</span></span><span>olve one equation for either variable. I'll use the first equation because its easier to solve for one of the variables. I'll be solving for y because that will allow us to solve for the value of x faster.
</span>x+y=60
y=60-x

2) Substitute what you get into the other equation:
20x + 5y = 600
20x + 5(60-x) = 600

3) Solve your new equation in step 2 for the variable, x.
20x + 5(60-x) = 600
20x + 300-5x = 600
15x + 300 = 600
15x = 300 
x=20

There are D) 20 $20 bills in her drawer. 

3 0
2 years ago
Which type of transformation creates a shape where only the angles are congruent to the original shape?
polet [3.4K]

D dilation -  because they increase/decrease the size of the object but retain its shape.

A, B and C all retain  the shape and the size.

4 0
3 years ago
Read 2 more answers
Other questions:
  • MARK AS BRAINLIEST!
    14·2 answers
  • Olivia works 4 hours more each week than her coworker Lily. Olivia works a total of 32 hours every 2 weeks. How many hours each
    12·1 answer
  • Help me please I need help on this question
    9·1 answer
  • Find all points on the y-axis that are a distance 6 from p(4, 7).
    14·1 answer
  • The difference of 2 numbers is 2 and their product is 80<br>Please respond quick
    15·2 answers
  • suppose a chord of a circle is 18 in. long and is 40 in. from the center. Find the length of the radius.
    12·2 answers
  • 25 pts and a mark for real answers. Help!! A store is having a sale on chocolate chips and walnuts. For 5 pounds of chocolate ch
    14·1 answer
  • If a system of linear equations has an infinite number of solutions, what do you know about the graph of the system?
    6·1 answer
  • What is the slope (16,-17) and (4,-13)
    10·1 answer
  • The St. Croix junior hockey
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!