a sample of radioactive isotope had an initial mass of 800 mg in the year 2000 and decays exponentially better over time. a measurement in the year 2005 found that the sample’s mass had decayed to 190 mg. what would be the expected mass of the sample in the year 2009, to the nearest whole number?

Answers

Answer 1

Answer:

The expected mass of the sample in the year 2009 is approximately 60 miligrams.

Step-by-step explanation:

The mass of radioactive isotopes decays exponentially in time, the equation that represents this phenomenon is presented below:

[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex] (1)

Where:

[tex]m(t)[/tex] - Current mass of the radioactive isotope, in miligrams.

[tex]m_{o}[/tex] - Initial mass of the radioactive isotope, in miligrams.

[tex]t[/tex] - Time, in years.

[tex]\tau[/tex] - Time constant, in years.

First, we must find the time constant associated to the decay of the radioactive isotope by clearing the respective term in (1):

[tex]-\frac{t}{\tau} = \ln \frac{m(t)}{m_{o}}[/tex]

[tex]\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }[/tex]

If we know that [tex]t = 5\,y[/tex], [tex]m(t) = 190\,mg[/tex] and [tex]m_{o} = 800\,mg[/tex], then the time constant is:

[tex]\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }[/tex]

[tex]\tau = -\frac{5\,y}{\ln \frac{190\,mg}{800\,mg} }[/tex]

[tex]\tau \approx 3.478\,y[/tex]

Now, we calculate the mass of the radioactive isotope in 2009 ([tex]t = 9\,y[/tex]). If we know that [tex]t = 9\,y[/tex], [tex]\tau \approx 3.478\,y[/tex] and [tex]m_{o} = 800\,mg[/tex], then the mass of the radioactive isotope is:

[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex]

[tex]m(9\,y) = (800\,mg)\cdot e^{-\frac{9\,y}{3.478\,y} }[/tex]

[tex]m(9\,y) \approx 60.155\,mg[/tex]

The expected mass of the sample in the year 2009 is approximately 60 miligrams.


Related Questions

Look at this graph: What is the equation of the axis of symmetry?

Answers

9514 1404 393

Answer:

  x = -6

Step-by-step explanation:

The curve is symmetrical about the vertical line through the minimum point. That minimum is 6 grid squares left of the y-axis, so the equation is ...

  x = -6

In circle A as shown below, segment DC is tangent to circle A at D. Also, DC = 4 and BC = 2
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Step-by-step explanation:

for khan academy math please answer, thank you!

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Answer:

7pi/theta = radius

Step-by-step explanation:

So we are using the arc length, central angle(in radians), and radius.

We know arc length, which is 7pi.

We don't know theta, which does not matter.

And finally, we don;t know radius, which is what we are looking for.

To find radius, we use:

arc length/theta=radius

Lets plug in our values:

7pi/theta=radius.

So the answer to the khan acadamy question is

7pi/∅

Here are some othr things that may help:

Radian * Radius = arc length

This solves for arc length

Here is another one:

Arc length/radius= radian

This solves for radians

Hope these help! :)

HELP asap now lol lorf

Answers

Answer:

[tex]22\ km[/tex]

Step-by-step explanation:

One is given the following information:

[tex]10\frac{1}{1}[/tex] km were covered on Thursday[tex]10\frac{1}{1}[/tex] km were covered on Friday

One is asked to find the total distance covered on both of these days. In order to do so, one must remember in a fraction, any number over (1) is equal to the numerator (number over the fraction bar). Thus one can form the following equation:

[tex](Thursday)+(Friday) = Total\ distance[/tex]

Substitute,

[tex](Thursday)+(Friday) = Total\ distance[/tex]

[tex](10\frac{1}{1})+(10\frac{1}{1}) = Total\ distance[/tex]

Simplify,

[tex](10\frac{1}{1})+(10\frac{1}{1}) = Total\ distance[/tex]

[tex](10+1)+(10+1) = Total\ distance[/tex]

[tex](11)+(11)=Total\ distance[/tex]

[tex]11+11=Total\ distance[/tex]

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Find an expression which represents the sum of (-8x+7y)(−8x+7y) and (2x-2y)(2x−2y) in simplest terms.

Answers

Answer:

Step-by-step explanation:

(-8x+7y)(-8x+7y)+(2x-2y)(2x-2y)

=64x²-56xy-56xy+49y²+(4x²-4xy-4xy+4y²)

=64x²-112xy+49y²+4x²-8xy+4y²

=68x²-120xy+53y²

(x + 6)² + (y - 2)² = 100. What is the center of the circle? What is the radius of the circle?

Answers

Answer:

Step-by-step explanation:

"100" or any constant at the end of the equation is r² (radius squared). So, the radius is 10.

the center of the circle is (-6, 2)

the equation template of a circle is (x -h)² + (y - k)² = c

(h,k) is the center of the cirlce.

Center: (-6,2)
Radius: 10

Mhanifa can answer this only

I don't understand
8x + 2y = 104
Is that possible, and if so, prove it pls
Mhanifa is the best user on Brainly
So, if I attract him, I will die

Answers

Answer:

Implicit Form: 4x + y - 52 = 0

Step-by-step explanation:

8x + 2y = 104 => Move constant to the left and change the sign

8x + 2y - 104 = 0 => Divide both sides of the equation by 2

4x + y - 52 = 0

Hope this helps!

Iva del 21% de 150=
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Answers

Si es 150 es precio sin IVA, tu precio con IVA sería de 181.5. La cantidad del IVA sería de 31.5

malia and her sister walk at a constant rate of 4 miles per hour how far can malia and her sister walk in 1.5 hours

please i need help now.​

Answers

6 miles 4x1.5=6 hope this helps

Can someone help me?

Answers

Answer:

0 h= 0 mi

1 h = 60 mi

2 h = 120 mi

3 h = 180 mi

Distance: 0, 60, 120, 180

Multiple 60 by the number of x

Area of parts of circles
You might need: Calculator
2
Find the area of the semicircle.
Either enter an exact answer in terms of or use 3.14 for T and enter your answer as a decimal.
units

Answers

Area of semicircle = (πr²) ÷ 2


Area of semicircle:
= (3.14)(2)² ÷ 2

= (3.14)(4) ÷ 2

= 12.56/2

= 6.28

What do the three red tiles in the model of the equation below represent?
=
1
-3
3
ОООО
-Зх

Answers

Step-by-step explanation:

There are 3 times of -x

which means the total of those x

=

[tex]3 \times ( - x) \\ = - 3x[/tex]

Series:

Use the Arithmetic Series formula to calculate the sum:

-6+(-3)+0+ • • • + 162

(Hint: how many numbers are being added?)

Answers

Answer:

Step-by-step explanation:

The common difference is 3.

nth term = -6+(n-1)3

-6+(n-1)3 = 162

(n-1)3 = 168

n-1 = 56

n = 57

162 is the 57th term.

S₅₇ = 57×(a_1+a_{57})/2

= 57×(-6+162)/2

= 57×156/2

= 57×78

= 57×(-6+162)/2

= 4446

Please help with this question!!!!!

Answers

72 in2 because you add the area of everything

I keep getting this wrong. I got f(x)=1/2^x

Answers

Answer:

Try that....

[tex]f(x) = \frac{1}{ {5}^{x} } [/tex]

Step-by-step explanation:

I hope that is useful for you :)

A square mirror has an area of 25 square feet. How long is each edge of the mirror?

Answers

Each edge is 5 feet.
———-
The length is 5 and the width as well. To find the area of the square mirror, you would multiply each side to get 25 ft squared. See attached image for more details.

A running track has two semi-circular ends with radius 25m and two straights of length 87.6m as shown.
Calculate the total distance around the track rounded to 1 DP.

Answers

The total distance around the track is 332.2 meters

How to calculate the total distance?

The complete question is in the attached image

The given parameters are:

Radius, r = 25 m

Length, l = 87.6 m

Start by calculating the circumference of the two semi-circular ends using:

[tex]C = 2\pi r[/tex]

So, we have:

C = 2* 3.14 * 25

Evaluate

C = 157

The total distance around the track is then calculated as:

Total = 2l + C

This gives

Total = 2 * 87.6 + 157

Evaluate

Total = 332.2

Hence, the total distance around the track is 332.2 meters

Read more about perimeter at:

https://brainly.com/question/24571594

#SPJ1

How many times larger is the value of 42.38 compared to 4.238

Answers

Answer:

10 times larger

Solve for x

2 (x + 1) = -200 x= 66

2x + (-3) = = (-23) x=

X - 3 = (-9) x=

(-3x) - 5 = 16 x=

-4 (y - 2) = 12 x=

4x = (-28) x=

2x + 9 = (-15) x=

X + 5 = 18

3 (x+ 5) = 18

3x + 5 = 18

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20.8 = 4 (z + 1.1)

3 (x + 4.5) = 36

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14 = 2 (x + 3)

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Answers

Answer:

---------

Step-by-step explanation:

x-3= -9

x= -9/ 3

x= -3

( -3x)-5 =16

-3x = 16+5

×= 21/-3

x = -7


In ABC with the right angle at vertex C, sin(b)= (26)/8. What is sin(a)?

Answers

Answer:

We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts.

Step-by-step explanation:

Pythagorean theorem:   a2 + b2 = c2.

Sines:   sin A = a/c, sin B = b/c.

Cosines:   cos A = b/c, cos B = a/c.

Tangents:   tan A = a/b, tan B = b/a.

Which of the following is the surface area of the right cylinder below?
O A. 480pi units2
O B. 204pi units2
O c. 408pi units2
O D. 240pi units2

Answers

Answer:

The answer is D.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

there are 45 students In a class if 60% of them are girls and 40% of them are boys find the number of girls and boys​

Answers

Answer:

27 girls and 18 boys

Step-by-step explanation:

you need to divide the 45 pupils into 60 and 40 percent to

use a ratio to compare this quantity 25mm : 2cm

Answers

5:4 i’m not quite sure but i think it would be 5:4

What is the value of 3/4

Answers

Answer:

0.75

0.25 less than 1

Step-by-step explanation:

i dont get it

Answer:

0.75 is the answer

2 (-3x-4) >16
Solve the inquality for X

Answers

Answer:

x < -4

Step-by-step explanation:

2(-3x - 4) > 16

-6x - 8 > 16

-6x > 16 + 8

-6x > 24

-x > 4

x < -4

Answer:

x < -4

Step-by-step explanation:

2(-3x - 4) > 16

Distribute.

-6x - 8 > 16

Add 8 to both sides.

-6x > 24

Divide by -6. When dividing by a negative, flip the sign.

x < -4.

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Answers

Answer:

18/999

Step-by-step explanation:

Answer:

2/111 = 18/999

write an explicit formula for an, the nth term of the sequence 11,2,-7

Answers

Answer:

[tex]a_{n}[/tex] = 20 - 9n

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 2 - 11 = - 7 - 2 = - 9

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 11 and d = - 9 , then

[tex]a_{n}[/tex] = 11 - 9(n - 1) = 11 - 9n + 9 = 20 - 9n

What’s the answer for this question

Answers

Answer:

dvdvsdv

Step-by-step explanation:

dsvfvdfvdv

Sisiennskskwskasnnwna

A drawing of a house is 8.5 inches tall. Enter the height of the house in feet.
HELP PLSSSS I REALLY APPRECIATE IT!

Answers

Answer:

.70833

Step-by-step explanation:

Divide 8.5 by 12 since there are 12 inches in 1 foot

Answer:

.71 feet

Step-by-step explanation:

If you need an explanation then let me know in comments

plss help i’ll give brainliest thank you!

Answers

Answer:

p

Step-by-step explanation:

Absolute value cancels negative so the greatest would be P.

have a nice day and i hope this helps! <3

P because absolute value cancels negative so it’d just be positive 6
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