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
Orlov [11]
3 years ago
15

Cesium-137 has a half-life of about 30 years. A) Find the annual decay rate and round final result to 4 decimal places. B) Find

the continuous decay rate and round final result to 4 decimal places. C) How long will it take for a 10 gram sample to decay to 1 gram? Round to nearest year and interpret your result with a complete sentence. D) Complete this statement: as x goes to infinity, y goes to ___.
Mathematics
1 answer:
MrMuchimi3 years ago
8 0

Answer:

  • 0.0228
  • 0.0231
  • 100 years
  • 0

Step-by-step explanation:

The exponential equation for the fraction remaining after x years can be written as ...

  y = (1/2)^(x/30)

A) For x=1, the fraction remaining is ...

  y = (1/2)^(1/30) ≈ 0.97716 = 1 - 0.0228

Of the original amount, 0.0228 decays each year.

__

B) The continuous decay rate is the natural log of the growth factor, so is ...

  ln(0.97716) = -0.0231

The continuous decay rate is 0.0231 of the present amount (per year).

__

C) For y=.10 (1/10 of the original amount) we find x to be ...

  .1 = .5^(x/30)

  ln(.1) = (x/30)ln(.5) . . . . . take the natural log

  30ln(0.1)/ln(0.5) = x ≈ 100 . . . years

It will take 100 years for a 10-gram sample to decay to 1 gram.

__

D) As x goes to infinity, y goes to zero.

_____

The relationship between growth rate and growth factor is ...

  growth factor = 1 + growth rate

When the growth rate is negative, it is called a decay rate.

You might be interested in
Solve the equation 7h-5(3h-9)=-72
STALIN [3.7K]
H=14 is your answer.

3 0
3 years ago
Read 2 more answers
The figure shows a grid consisting of 25 small equilateral triangles. How many diamonds, consisting of two adjacent small triang
DerKrebs [107]

There are 30 diamonds in total.

8 0
2 years ago
Can someone plz help me ASAP thxs
allsm [11]

Answer:

352

Step-by-step explanation:

8 x 6 x 8 = 384

384- (4 x 1 x 8)

384-32=352

6 0
3 years ago
If c is the curve given by \mathbf{r} \left( t \right = \left( 1 5 \sin t \right \mathbf{i} \left( 1 3 \sin^{2} t \right \mathbf
jonny [76]
With the curve C parameterized by

C:\mathbf r(t)=\underbrace{15\sin t}_{x(t)}\,\mathbf i+\underbrace{13\sin^2t}_{y(t)}\,\mathbf j+\underbrace{12\sin^3t}_{z(t)}\,\mathbf k

with 0\le t\le\dfrac\pi2, and given the vector field

\mathbf f(x,y,z)=x\,\mathbf i+y\,\mathbf j+z\,\mathbf k

the work done by \mathbf f on a particle moving on along C is given by the line integral

\displaystyle\int_C\mathbf f\cdot\mathrm d\mathbf r=\int\limits_{t=0}^{t=\pi/2}\mathbf f(x(t),y(t),z(t))\cdot\frac{\mathrm d\mathbf r(t)}{\mathrm dt}\,\mathrm dt

where

\mathrm d\mathbf r=(15\cos t\,\mathbf i+26\sin t\cos t\,\mathbf j+36\sin^2t\cos t\,\mathbf k)\,\mathrm dt

The integral is then

\displaystyle\int_0^{\pi/2}(15\sin t\,\mathbf i+13\sin^2t\,\mathbf j+12\sin^3t\,\mathbf k)\cdot(15\cos t\,\mathbf i+13\sin2t\,\mathbf j+18\sin t\sin2t\,\mathbf k)\,\mathrm dt
=\displaystyle\int_0^{\pi/2}(432\sin^5t\cos t+338\sin^3t\cos t+225\sin t\cos t
=269
6 0
3 years ago
5. Describe the pattern below.<br> 9, 12, 15, 18, 21, 24
Dafna11 [192]

Answer:

The numbers increase by 3

Step-by-step explanation:

The difference between all the numbers in the sequence have a gap of 3

9 and 12 --gap of 3

12 and 15--gap of 3

18 and 21--gap of 3

21 and 24--gap of 3

6 0
3 years ago
Read 2 more answers
Other questions:
  • Just need answer, that fills in the blanks, i dont need work shown ty<br> will give brainly!!
    14·1 answer
  • Does anyone know this????
    11·1 answer
  • 9- 3x - (-8y) + 9x - y Solve pleaseee
    13·1 answer
  • Please help, giving 15 points
    14·1 answer
  • If cos(2/3(x) + 20) ° = sin(2x – 10)”, find the acute angles of the corresponding right triangle.
    11·2 answers
  • Find the supplement of 2/3of a right angle​
    7·1 answer
  • ellie wanted to order candy online. company A us offering 2 1/2 pounds of chocolate for $32.50; while company B is offering 2 3/
    9·1 answer
  • Find area of this figure 3 ft 4 ft 5ft
    9·1 answer
  • I need help figuring out the answers for this
    11·1 answer
  • Which function has an inverse that is also a function? y = 3 2 - 5 3 y = 322 y= x - y = 322 – 5x + 3
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!