$2,500 is invested in an account earning 8.4% interest compounded annually. How many years did it take to reach $4,000?

Answer:

a) [tex]k \approx 0.0602\,\frac{1}{min}[/tex] ([tex]k\approx 6.02\,\frac{\%}{min}[/tex]), b) [tex]k \approx 0.0648\,\frac{1}{min}[/tex] ([tex]k \approx 6.48\,\frac{\%}{min}[/tex]), c) [tex]t_{1/2} \approx 60.274\,days[/tex], d) [tex]t_{1/2}\approx 4.305\,min[/tex], e) [tex]k \approx 0.3\,\frac{1}{min}[/tex] ([tex]k\approx 30\,\frac{\%}{min}[/tex]), f) [tex]k \approx 0.0120\,\frac{1}{min}[/tex] ([tex]k \approx 1.20\,\frac{\%}{min}[/tex]), g) [tex]k \approx 2.876\times 10^{-5}\,\frac{1}{yr}[/tex] ([tex]k \approx 2.876\times 10^{-3}\,\frac{\%}{yr}[/tex])

Step-by-step explanation:

All radioactive isotopes decay exponentially, the mass of the isotope as a function of time ([tex]m(t)[/tex]), measured in grams, is defined by:

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

Where:

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

[tex]k[/tex] - Decay rate, measured in [tex]\frac{1}{min}[/tex] or [tex]\frac{1}{day}[/tex] or [tex]\frac{1}{yr}[/tex].

[tex]t[/tex] - Time, measured in minutes, days or years.

We define the decay rate in terms of half-life by using the following expression:

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

Where [tex]t_{1/2}[/tex] is the half-life of the isotope, measured in minutes or years.

Now we proceed to determine the missing values:

a) Polonium-200 ([tex]t_{1/2} = 11.5\,min[/tex])

[tex]k = \frac{\ln 2}{11.5\,min}[/tex]

[tex]k \approx 0.0602\,\frac{1}{min}[/tex]

b) Lead-194 ([tex]t_{1/2} = 10.7\,min[/tex])

[tex]k = \frac{\ln 2}{10.7\,min}[/tex]

[tex]k \approx 0.0648\,\frac{1}{min}[/tex]

c) Iodine-125 ([tex]k = 0.0115\,\frac{1}{day}[/tex])

[tex]t_{1/2} = \frac{\ln 2}{k}[/tex]

[tex]t_{1/2} = \frac{\ln 2}{0.0115\,\frac{1}{day} }[/tex]

[tex]t_{1/2} \approx 60.274\,days[/tex]

d) Kryption-75 ([tex]k = 0.161\,\frac{1}{min}[/tex])

[tex]t_{1/2} = \frac{\ln 2}{k}[/tex]

[tex]t_{1/2} = \frac{\ln 2}{0.161\,\frac{1}{min} }[/tex]

[tex]t_{1/2}\approx 4.305\,min[/tex]

e) Strontium-79 ([tex]t_{1/2} = 2.3\,min[/tex])

[tex]k = \frac{\ln 2}{2.3\,min}[/tex]

[tex]k \approx 0.3\,\frac{1}{min}[/tex]

f) Uranium-229 ([tex]t_{1/2} = 58\,min[/tex])

[tex]k = \frac{\ln 2}{58\,min}[/tex]

[tex]k \approx 0.0120\,\frac{1}{min}[/tex]

g) Plutonium-239 ([tex]t_{1/2} = 24100\,yr[/tex])

[tex]k = \frac{\ln 2}{24100\,yr}[/tex]

[tex]k \approx 2.876\times 10^{-5}\,\frac{1}{yr}[/tex]

Answer:

A

explanation:

When something has a constant rate of change, one quantity changes in relation to the other by a constant factor. One concrete example of this is the relation of distance rate and time

Answer:

c is the correct answer i think not sure

Answer:

a+3300=b

5a+3300=6a

minus 5a both sides

a=3300

3300*5=16500

3300*6=19800

16500+19800=36300

$36,300

Answer: 1) $0.76 per serving of pumpkin pie

2) 64 people

3)

1 1/3 cup sweet potatos

2 tablespoons + 2 teaspoons of white sugar

1 egg

1/4 teaspoon of salt

2 tablespoons of butter

2 tablespoons + 2 teaspoons of milk

1/4 teaspoon of vanillia

2 tablespoons + 2 teaspoons of brown sugar

1 tablespoon + 2 1/3 teaspoons flour

2 tablespoons + 2 teaspoons of peacans

Step-by-step explanation:

1) the total cost of the ingredients needed to prepare a pumpkin pie = $1.50 + ($2.59 / 6) + ($5.99 / 6) + $1.25 + ($3.79 / 2) = $6.075

if we cut 8 servings per pie, then the cost per serving = total cost of the pie/number of servings = $6.075 / 8 = $0.759375 ≈ $0.76 per serving of pumpkin pie

2) 1lb=16oz

24/6=4

4x16=64

Answer:

0.76 per serving of pumpkin pie

2) 64 people

Step-by-step explanation:

Answer:

y = 3x + 5

Step-by-step explanation:

The zero seems to be a place holder to mess you up. Just ignore that it doesn't do anything. Add -3x and -5 to the both sides to create y = 3x + 5

Answer:

x = -6 and x = 12 are parallel

Step-by-step explanation:

they are both vertical lines, one crosses the x-axis at -6, the other at 12

Answer:

c

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

all you have to do is divide 12 by 3

Answer:

4 if ur doing division or 3 over 12

Step-by-step explanation:

Answer:

12.231

Step-by-step explanation:

you add them with the zeros

Answer:

12.231

Step-by-step explanation:

0.031+10+2.2

10.031+2.2

12.231

Answer:

Irrational means it can not be written completely. If there was a line above the last number/the number was infinite, it would be irrational. But because it stops, its not irrational. It can be written as a fraction, so it is rational.

Answer:

4

Step-by-step explanation:

–x + 6 = 0.5x

–(4) + 6 =.5(4)=2

-x-.5x=-6

-1.5x=-6

X=4

Answer:

x=4

Step-by-step explanation:I took the test

Answer:

correct answer it's A

give me a like at least please

Answer:

the answer is A on edge 2020

Step-by-step explanation:

hope this helped:)

Answer:

Your answer is A.

Step-by-step explanation:

Answer:

m = 2

Step-by-step explanation:

[tex]m=\frac{rise}{run}=\frac{13-5}{6-2}=\frac{8}{4}=\boxed{2}[/tex]

Hope this helps.

Answer:

uhhh

Step-by-step explanation:

Answer:

This question is to perfect to answer.

Answer:

7x-21

Step-by-step explanation:

Answer:

$20 + $15m ≥ $80

Step-by-step explanation:

He starts off with $20.

He adds $15 each month, so $15m.

He wants to save at least $80, which means greater than or equal to $80. So, you use this symbol: ≥

Put it all together.

$20 + $15m ≥ $80

Hope that helps.

Answer:

True

Step-by-step explanation:

Set up the problem in slope intercept i.e y = mx + b. Add 4x to both sides to create y = 4x -2.  Any number or fraction in the m part is the slope. So the slope is 4.

True, the slope of the line y - 4x = -2 is 4.

The equation of a line in slope-intercept form with slope m is,

y = mx + c

Where 'c' is the y-intercept of the line.

Given that,

The equation of a line is,

y - 4x = - 2

Now it can be written in a slope-intercept form as,

y - 4x = - 2

Add 4x on both sides,

y - 4x + 4x = - 2 + 4x

y = 4x - 2

By comparing with slope - intercept of the equation,

Slope (m) = 4

Therefore, the statement is true.

To learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ6

Answer:

ok im convuzed how do you buy a 90ft tree cuz that sounds fun

Step-by-step explanation:

pls lemme know

Answer:

Option (2)

Step-by-step explanation:

Given sequence is,

8, 24, 72, 216........

1st term of the sequence 'a' = 8

Ratio of 2nd and 1st term = [tex]\frac{24}{8}=3[/tex]

Ratio of 3rd and 2nd term = [tex]\frac{72}{24}=3[/tex]

There is a common ratio of 'r' = 3 in each successive and previous term.

Therefore, it's a geometric sequence.

Since, nth term of a geometric sequence is given by,

[tex]T_n=a(r)^{n-1}[/tex]

Therefore, function representing the geometric sequence is,

f(n) = [tex]f(n)=8(3)^{n-1}[/tex]

Option (2) is the answer.

Answer:

Christina has 30 quarters and 20 dimes.

Step-by-step explanation:

Given that a quarter is worth 0.25 dollars and a dime is worth 0.10 dollars, if Christina has 50 coins and these add up to a total of $ 9.50, to determine the number of quarters and dimes that she has in her possession, the following calculation must be carried out, taking into account that the difference between a quarter and a dime is 0.15 dollars:

50 x 0.25 = 12.5

12.5 - 9.5 = 3

Thus, the difference between the value that Christina has and the value that she would have if all of her coins were quarters is 3 dollars. Thus, since 0.15 x 20 equals 3, of the 50 coins Christina has, 30 are quarters and 20 are dimes.

This is confirmed through the following equation:

30 x 0.25 + 20 x 0.1 = X

7.5 + 2 = X

9.5 = X

Answer:

1.08

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

1.01<1.08<1.17<1.20

Answer:

you didnt add the attachment

Answer:

125 hamburgers

Step-by-step explanation:

Let x be the number of hamburgers sold and 3x the number of cheeseburgers sold.

So:

x+3x=500

4x=500

x=125

So there are 125 hamburgers sold.

Answer:

3 +9 does not belong because it doesn't equal 10 like the rest of them do.

Answer:

3

Step-by-step explanation:

3 times 30 = 90 then divide 90 and 30 you get 3

Answer:

it is 0 so that is x

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The number of tips that the server gets is dependent on how many customers she serves.

Hope this helps!

Answer:

i dont understand

Step-by-step explanation:

but probably c

Answer:

I don't know how to draw it out but...

Step-by-step explanation:

For every 3 kids there is 1 candy bar. For every 2 candy bars there are 6 kids. 2 candy bars divided by 6 kids equals, a third of a candy bar per kid.

Answer:

the water rises 50ft  per minute so for 60min you have to multiply 60 x 50 which will be 3000ft in 60mins

Step-by-step explanation: