Element X is a radioactive isotope such that every 13 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 90 grams, how long would it be until the mass of the sample reached 62 grams, to the nearest tenth of a year?

Answers

Answer 1

Answer:

The mass of Element X will reach 62 grams in 7.0 years.

Step-by-step explanation:

We can find the time of decay of Element X by using the exponential decay equation:

[tex] \frac{dm}{dt} = -\lambda t [/tex]

The solution of the above equation is:

[tex]m_{(t)} = m_{0}e^{-\lambda t}[/tex]     (1)

Where:  

t: is the time =?

λ: is the decay constant                                                                                        

[tex]m_{(t)}[/tex]: is the mass at time t = 62 grams

[tex]m_{0}[/tex]: is the initial mass = 90 grams

First, we need to calculate λ

[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex]   (2)    

Where [tex]t_{1/2}[/tex] is the half-life = 13 years

By entering equation (2) into (1) and solving for "t" we have:

[tex]\frac{m_{(t)}}{m_{0}} = e^{-\frac{ln(2)}{t_{1/2}}*t}[/tex]    

[tex]ln(\frac{m_{(t)}}{m_{0}}) = -\frac{ln(2)}{t_{1/2}}*t[/tex]      

[tex]t = -ln(\frac{m_{(t)}}{m_{0}})(\frac{t_{1/2}}{ln(2)}) = -ln(\frac{62}{90})(\frac{13}{ln(2)}) = 7.0 y[/tex]  

Therefore, the mass of Element X will reach 62 grams in 7.0 years.

I hope it helps you!


Related Questions

Write each expression using exponents.
3/8 * 3/8 * 3/8=

Answers

Answer:

3/8^3

Step-by-step explanation:

the exponent is 3

Answer:

(3/8)^3

3^3 * 2^-9

Step-by-step explanation:

3/8 * 3/8 * 3/8 = (3/8)^3

= 3^3 * (1/8)^3 = 3^3 * (2^-3)^3 = 3^3 * 2^-9

Can you help me with these questions

Answers

Answer:

7) Unfilled dot at 5 with a line going right

8) A filled dot at 8 with a line going right

9) Unfilled dot at 22 with a line going left

10) A filled dot 13 with a line going left

11) x < 9

12) x > 14

13) x ≤ 11

14) x ≥ 7

Step-by-step explanation:

> means greater than

≥ means greater than or equal to

< means less than

≤ means less than or equal to

If something is greater than the given number then the variable increases in value and will be on the right side of the number line

If something is less than the given number then the variable decreases in value and will be on the left side of the number line

If a variable is < or > the dot is unfilled because it does not include that number

If a variable is ≤ or ≥ the dot is filled because it includes the given number

I need help

An amount of $16,000 is borrowed for 8 years at 7.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?

Answers

Answer:

$28009.05

Step-by-step explanation:

Let us use the formula A = P(1 + r/n)^(nt)

Step 1: Convert 7.25 to decimal

[tex]7.25\% = 0.0725[/tex] in decimal form

Step 1: Percent means 'per 100'. So, 7.25% means 7.25 per 100 or simply 7.25 over 100. [tex]7.25 \div 100\\\\= \frac{7.25}{100}\\\\= 0.0725[/tex] If you divide 7.25 by 100, you'll get 0.0725 (a decimal number).

Step 2: Solve with the formula

[tex]A = 16000(1 + 0.0725)^8\\\\A= 28009.05[/tex]

Step 1: Add the numbers: [tex]1+0.0725=1.0725[/tex][tex]=16000\cdot \:1.0725^8[/tex][tex]=16000\cdot \:1.75056[/tex]Step2: Multiply[tex]=28009.05068[/tex]

the sum of three consecutive natural number is 30 find the numbers​

Answers

Answer:

9 + 10 + 11

Step-by-step explanation:

guess and check

Answer:

9,10,and 11

Step-by-step explanation:

The triangles have a scale of 3: 5. What is the value of a? *

Answers

Answer:

Step-by-step explanation:

multiply the ratio by 24/5 and you have

72/5 : 24

or

14.4:24

Y/3+y/4=5/6
Find the LCD that would eliminate the fractions

Answers

Answer:

the answer is in the picture

Which values are equivalent to the fraction below? Check all that apply

4 5/4 7

Answers

Answer:

the answer is the 4/-2

Step-by-step explanation:

you can understand from the answer

how is 2/5 + 3/5 = 1

Answers

Answer:

Hey mate......

Step-by-step explanation:

This is ur answer.....

= 2/5 + 3/5 = 5/5 = 1

(When you simplify both numbers, you get 1)

Hope it helps!

Brainliest pls!

Follow me! :)

Imagine cutting up a pizza into 5 slices

If you take 2 slices, then you take 2 out of the 5, so the fractional amount you took is 2/5 of the full pizza.

If your friend takes 3 slices, then she or he takes 3/5 of the full pizza

Adding the two fractional amounts should get us back to 1 full pizza, which is why 2/5+3/5 = 1.

-----------

We could say this:

2/5 + 3/5 = (2+3)/5 = 5/5 = 1

Dividing any number over itself, as long it's not zero, always leads to 1.

So that's why 5/5 = 1.

Write the standard equation of each circle below

Answers

Okay so if you answer me in the comments I can help you but I need more explanation than that :)

Order these numbers from least to greatest.

7.13, 7.013, 7.2, 7.1371

Answers

Answer:

7.013, 7.13, 7.1371, 7.2

Step-by-step explanation:

i will give brainliest!! please help me, i appreciate it !!

Answers

Answer:

-4050

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Step-by-step explanation:

Step 1: Define

Identify

6x²y³ - 2x + 10

x = 5

y = -3

Step 2: Evaluate

Substitute in variables:                                                                                     6(5)²(-3)³ - 2(5) + 10Exponents:                                                                                                        6(25)(-27) - 2(5) + 10Multiply:                                                                                                             -4050 - 10 + 10Add:                                                                                                                   -4050

Please help with this

Answers

The answers would be: B, D, and E


help fast please lol

Answers

Answer:

Between 0 and 3: decreasing

Between 3 and 4: constant (stays the same)

Between 4 and 8: decreasing

Step-by-step explanation:

Find a.

Write your answer in simplest radical form.

Answers

Answer:

[tex]a=10[/tex]

Step-by-step explanation:

This problem can be solved in a ridiculous number of ways. However, it is likely introduced as a special-triangle problem in this question, because 4 pieces of information are given opposed to the necessary 3 to solve the triangle.

Special Right Triangles:

In any 30-60-90 triangle, all sides are in the proportion [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse and [tex]x[/tex] is the side opposite to the 30 degree angle. Since we notice that the side we're solving for is directly opposite to the 30 degree angle, we know that the side marked [tex]10\sqrt{3}[/tex] must be [tex]x\sqrt{3}[/tex] and therefore we have [tex]a=\boxed{10}[/tex]

Four coins are tossed in succession. What is the probability of getting all heads?

1/4
1/2
1/16

Answers

Answer:

1/16

Step-by-step explanation:

There is a 1/2 chance to flip a heads.

So, in this case, we would multiply 1/2 four times in reference to the coins being flipped a total of 4 times to find its probability.

1/2 x 1/2 x 1/2 x 1/2 = 1/16

Thus, there is a 1/16 chance that you'd get heads four times in a row.

Answer:
1/16
Step by Step Explanation:
The reason being is that all the chances will be 1/2 so you need to multiply 1/2x1/2x1/2x1/2

Through: (-3,1), slope = 2

Answers

Answer:

y = 2x + 7

Stepy by-step explanation:

y = 2x + b

1 = 2(-3) + b

1 = -6 + b

7 = b

Please help me out with this problem :)

Find the maximum value of P= x + 6y subject to the following constraints

Answers

Answer:

I cant tell what the answer is cause X and Y dont have a value

Step-by-step explanation:

Answer:

p=9

Step-by-step explanation:

Solve for x. Round to the nearest tenth, if necessary.
P
29°
х
Q
-6.6
R

Answers

Answer:

The x in this question is 151 degrees

Answer:

13.6

Step-by-step explanation:

find the area of the figure with coordinates A (-6,1), B (2,1), C(-3,4), D(5,4)

Answers

Answer: The area of the figure is 24 units.

Step-by-step explanation:

After plotting, the given points on the graph, we can observe that it is a parallelogram(opposite sides are equal and parallel)

Height = 4-1 = 3 units

Base = 2-(-6) = 8 units

Area of parallelogram = Base x height

= 8 x 3 square units.

= 24  square units.

Hence, the area of the figure is 24 units.

Find the sum of the first 40 terms of the arithmetic sequence: 16,24,32,40

Answers

Answer:

320 is the answer

Step-by-step explanation:

8x40=320


[tex]2x - 4 = 30[/tex]

Answers

Answer:

x=17

Step-by-step explanation:

2x-4=302x=30+42x=34x=34/2x=17

stay safe healthy and happy.

Answer:

x = 12

Step-by-step explanation:

2x - 4 = 30

2x = 30 + 4

2x = 34

x = 34/2

◆ x = 17

This is a Right answer

If f(y) = e^(9y) + e^(-9y), find f'(y). Use exact values.

Answers

Given:

[tex]f(y)=e^{9y}+e^{-9y}[/tex]

To find:

The f'(y).

Solution:

Chain rule of differentiation:

[tex][f(g(x))]'=f'(g(x))g'(x)[/tex]

Differentiation of exponential:

[tex]\dfrac{d}{dx}e^x=e^x[/tex]

We have,

[tex]f(y)=e^{9y}+e^{-9y}[/tex]

Differentiate with respect to y.

[tex]f'(y)=e^{9y}\dfrac{d}{dx}(9y)+e^{-9y}\dfrac{d}{dx}(-9y)[/tex]

[tex]f'(y)=e^{9y}\cdot 9(1)+e^{-9y}\cdot (-9)(1)[/tex]

[tex]f'(y)=9e^{9y}-9e^{-9y}[/tex]

Therefore, the differentiation of the given function is [tex]f'(y)=9e^{9y}-9e^{-9y}[/tex].

i need help!! im struggling with this question

Answers

Answer:

1 gallon : 25.6 miles

Step-by-step explanation:

So, the way we can find the rate, or ratio between 2 units is to divide one unit by the other unit.

So basically, we see the first set of units is:

2 gallons - 51.2 miles

So basically, for every 2 gallons, there are 51.2 miles.

To find the ratio, or rate, we must find the miles per gallon.

We can do that by dividing both sides by 2:(g=gallons, m=miles)

2g/2=51.2/2m

=

g=25.6

So for every gallon, there is 25.6 miles.

We can write this as:

1 : 25.6

Hope this helps!

Answer:

25.6

Step-by-step explanation:

51.2/2=25.6

Determine the value of x in the diagram.

Answers

The answer to the question is 114

−12 = 2 + 5v + 2v
help me plzzzzzzzzzzzz

Answers

Answer:

v = - 2

Step-by-step explanation:

Given

- 12 = 2 + 5v + 2v ( subtract 2 from both sides )

- 14 = 7v ( divide both sides by 7 )

- 2 = v

अब पछताए होत कया जब चिडिया चुग गई खेत अनुचछेद लिखिए​

Answers

Step-by-step explanation:

Go to the Indian Brainly.

I am Indian.

This question is worth 20 points and I will mark brainliest
which expressions are equivalent to 2 (3h + 7) choose "equivalent" or "Not equivalent" for each expression.


6h+7

2+3h+7

6h+7+7

3h+3h+14

(3h+7) + (3h+7)

Answers

Answer:

2(3h+7)

=6h+14

6h+7+7 (True)

3h+3h+14 (True)

Jack can program an app in 3 hours. Chris can program the same app in 8 hours. How long would it take them to program the same app working together?

Answers

Answer:

2 2/11 hours

Step-by-step explanation:

Let the number of hours

Jack spent programming his app = J

Chris spent programming his app = C

Total hours if they worked together = T

Hence,

1/T = 1/3 + 1/8

Lowest Common Denominator = 34

1/T = 8 + 3/24

1/T = 11/24

Cross Multiply

T × 11 = 1 × 24

T = 24/11

T = 2 2/11 hours

Therefore, it would take them to program 2 2/11 hours to program the same app working together

help please help me please​

Answers

Answer:

B

Step-by-step explanation:

Only 1 because

1/1 = 1

2/1 = 2

The answer can't be 0 because we can't divide by zero.

The answer can't be 2 because you can't divide 1 by 2 without having a number with decimal places

Same thing for the 4

The greatest common factor of 1 and 2 is 1.
The answer is B

Find the measure of angle C

Answers

Answer:

ajnasnnanananandbabbabbansbansbz svabsvsb

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