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
xxMikexx [17]
2 years ago
11

Element X is a radioactive isotope such that every 30 years, its mass decreases by half. Given that the initial mass of a sample

of Element X is 100 grams, how long would it be until the mass of the sample reached 64 grams, to the nearest tenth of a year?
Mathematics
1 answer:
Lena [83]2 years ago
8 0

Answer:

19.3 years

Step-by-step explanation:

Given that the initial mass of a sample of Element X is 100 grams,

The formula is given as:

N(t) = No × (1/2) ^t/t½

Element X is a radioactive isotope such that every 30 years, its mass decreases by half.

N(t) = Mass after time (t)

No = Initial mass = 100 grams

t½ = Half life = 30 grams

N(t) = 100 × (1/2) ^t/30

How long would it be until the mass of the sample reached 64 grams, to the nearest tenth of a year?

This means we are to find the time

N(t) = 100 × (1/2) ^t/30

N(t) = 64 grams

64 = 100(1/2)^t/30

Divide both sides by 100

64/100 = 100(1/2)^t/30/100

0.64 = (1/2)^t/30

Take the Log of both sides

log 0.64 = log (1/2)^t/30

log 0.64 = t/30(1/2)

t = 19.315685693242 years

Approximately = 19.3 years

You might be interested in
Solve for x and y:<br> 3/x -1/y =13/10<br> 1/x + 2/y =9/10
harkovskaia [24]

Answer:

  (x, y) = (2, 5)

Step-by-step explanation:

I find it easier to solve equations like this by solving for x' = 1/x and y' = 1/y. The equations then become ...

  3x' -y' = 13/10

  x' +2y' = 9/10

Adding twice the first equation to the second, we get ...

  2(3x' -y') +(x' +2y') = 2(13/10) +(9/10)

  7x' = 35/10 . . . . . . simplify

  x' = 5/10 = 1/2 . . . . divide by 7

Using the first equation to find y', we have ...

  y' = 3x' -13/10 = 3(5/10) -13/10 = 2/10 = 1/5

So, the solution is ...

  x = 1/x' = 1/(1/2) = 2

  y = 1/y' = 1/(1/5) = 5

  (x, y) = (2, 5)

_____

The attached graph shows the original equations. There are two points of intersection of the curves, one at (0, 0). Of course, both equations are undefined at that point, so each graph will have a "hole" there.

3 0
3 years ago
Aplicanso o teorema de pitagoras, determine a medida x indicada em cada um dos triângulos retângulos
Alina [70]
Applying or Pythagorean theorem, as determined by x indicated em um dos retângulos each Triangles. What do u mean
7 0
3 years ago
What is the result when x^3-2x^2+5x-13x 3 −2x 2 +5x−13 is divided by x-2x−2?
Aleksandr [31]

yo k se wey: rg`weaofjwafgEWF3WRF1QTFG3Q2TGF2

3 0
3 years ago
Mr. Dawson owns multiple fish breeding farms. The number of fish breeding farms is represented by the function f(x) = 5. The app
Ilya [14]
For this case what we must do is define h (x), which is given by:
 h (x) = f (x) * g (x)
 Where,
 f (x) = 5 (The number of fish breeding farms)
 g (x) = 80 (1.04) ^ x (The approximate number of fish per breeding farm)
 Substituting we have:
 h (x) = (5) * (80 (1.04) ^ x)
 Rewriting we have:
 h (x) = 400 (1.04) ^ x
 Answer:
 
the approximate population of the fish across all Mr. Dawson's farms after x months is:
 
h (x) = 400 (1.04) ^ x
7 0
3 years ago
Chris sells roses for $25.99 a bunch. At the end of the day he has collected $285.89. How many bunches of roses did he sell
Kryger [21]
11 bunches
In order to find how many bunches he sold, do 285.89/25.99
hope this helps!
3 0
3 years ago
Read 2 more answers
Other questions:
  • What is the simplified form of the following expression?<br> 6c^2 + 2.5d - d + 2c^2 - 3d
    8·1 answer
  • Does anyone know the answer?
    5·2 answers
  • A rocket was launched into the air from a podium 6 feet off the ground. The rocket path is represented by the equation h(t)=-16t
    11·1 answer
  • -8 is less than or equal to x, and -4 is greater than x ,as an inequality it is written as​
    15·1 answer
  • 150 adults complete a survey 80 are women the ratio of men and women in its simplest form
    13·2 answers
  • Se deposita 4000 soles a una tasa de interés del 0,8% quincenas .¿Que interes producirá en cinco quincenas?
    12·1 answer
  • Which equation represents this number sentence?
    12·1 answer
  • How would this be solved
    15·1 answer
  • <img src="https://tex.z-dn.net/?f=%20%5Chuge%20%5Ccal%20%5Ccolorbox%7Bpink%7D%7BQuestion%20%3A-%7D" id="TexFormula1" title=" \hu
    15·2 answers
  • The temperature was 6° C.<br> By how much has it fallen if it is now -5° C?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!