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Firlakuza [10]
3 years ago
12

The expression represents the cost of Janelle’s cell phone bill, where m represents the number of minutes of use.

Mathematics
1 answer:
Tcecarenko [31]3 years ago
5 0
12 since it stays the same
You might be interested in
Modeling Radioactive Decay In Exercise, complete the table for each radioactive isotope.
Julli [10]

Answer:

Step-by-step explanation:

Hello!

The complete table attached.

The following model allows you to predict the decade rate of a substance in a given period of time, i.e. the decomposition rate of a radioactive isotope is proportional to the initial amount of it given in a determined time:

y= C e^{kt}

Where:

y represents the amount of substance remaining after a determined period of time (t)

C is the initial amount of substance

k is the decaing constant

t is the amount of time (years)

In order to know the decay rate of a given radioactive substance you need to know it's half-life. Rembember, tha half-life of a radioactive isotope is the time it takes to reduce its mass to half its size, for example if you were yo have 2gr of a radioactive isotope, its half-life will be the time it takes for those to grams to reduce to 1 gram.

1)

For the first element you have the the following information:

²²⁶Ra (Radium)

Half-life 1599 years

Initial quantity 8 grams

Since we don't have the constant of decay (k) I'm going to calculate it using a initial quantity of one gram. We know that after 1599 years the initial gram of Ra will be reduced to 0.5 grams, using this information and the model:

y= C e^{kt}

0.5= 1 e^{k(1599)}

0.5= e^{k(1599)}

ln 0.5= k(1599)

\frac{1}{1599} ln 0.05 = k

k= -0.0004335

If the initial amount is C= 8 grams then after t=1599 you will have 4 grams:

y= C e^{kt}

y= 8 e^{(-0.0004355*1599)}

y= 4 grams

Now that we have the value of k for Radium we can calculate the remaining amount at t=1000 and t= 10000

t=1000

y= C e^{kt}

y_{t=1000}= 8 e^{(-0.0004355*1000)}

y_{t=1000}= 5.186 grams

t= 10000

y= C e^{kt}

y_{t=10000}= 8 e^{(-0.0004355*10000)}

y_{t=10000}= 0.103 gram

As you can see after 1000 years more of the initial quantity is left but after 10000 it is almost gone.

2)

¹⁴C (Carbon)

Half-life 5715

Initial quantity 5 grams

As before, the constant k is unknown so the first step is to calculate it using the data of the hald life with C= 1 gram

y= C e^{kt}

1/2= e^{k5715}

ln 1/2= k5715

\frac{1}{5715} ln1/2= k

k= -0.0001213

Now we can calculate the remaining mass of carbon after t= 1000 and t= 10000

t=1000

y= C e^{kt}

y_{t=1000}= 5 e^{(-0.0001213*1000)}

y_{t=1000}= 4.429 grams

t= 10000

y= C e^{kt}

y_{t=10000}= 5 e^{(-0.0001213*10000)}

y_{t=10000}= 1.487 grams

3)

This excersice is for the same element as 2)

¹⁴C (Carbon)

Half-life 5715

y_{t=10000}= 6 grams

But instead of the initial quantity, we have the data of the remaining mass after t= 10000 years. Since the half-life for this isotope is the same as before, we already know the value of the constant and can calculate the initial quantity C

y_{t=10000}= C e^{kt}

6= C e^{(-0.0001213*10000)}

C= \frac{6}{e^(-0.0001213*10000)}

C= 20.18 grams

Now we can calculate the remaining mass at t=1000

y_{t=1000}= 20.18 e^{(-0.0001213*1000)}

y_{t=1000}= 17.87 grams

4)

For this exercise we have the same element as in 1) so we already know the value of k and can calculate the initial quantity and the remaining mass at t= 10000

²²⁶Ra (Radium)

Half-life 1599 years

From 1) k= -0.0004335

y_{t=1000}= 0.7 gram

y_{t=1000}= C e^{kt}

0.7= C e^{(-0.0004335*1000)}

C= \frac{0.7}{e^(-0.0004335*1000)}

C= 1.0798 grams ≅ 1.08 grams

Now we can calculate the remaining mass at t=10000

y_{t=10000}= 1.08 e^{(-0.0001213*10000)}

y_{t=10000}= 0.32 gram

5)

The element is

²³⁹Pu (Plutonium)

Half-life 24100 years

Amount after 1000 y_{t=1000}= 2.4 grams

First step is to find out the decay constant (k) for ²³⁹Pu, as before I'll use an initial quantity of C= 1 gram and the half life of the element:

y= C e^{kt}

1/2= e^{k24100}

ln 1/2= k*24100

k= \frac{1}{24100} * ln 1/2

k= -0.00002876

Now we calculate the initial quantity using the given information

y_{t=1000}= C e^{kt}

2.4= C e^{( -0.00002876*1000)}

C= \frac{2.4}{e^( -0.00002876*1000)}

C=2.47 grams

And the remaining mass at t= 10000 is:

y_{t=10000}= C e^{kt}

y_{t=10000}= 2.47 * e^{( -0.00002876*10000)}

y_{t=10000}= 1.85 grams

6)

²³⁹Pu (Plutonium)

Half-life 24100 years

Amount after 10000 y_{t=10000}= 7.1 grams

From 5) k= -0.00002876

The initial quantity is:

y_{t=1000}= C e^{kt}

7.1= C e^{( -0.00002876*10000)}

C= \frac{7.1}{e^( -0.00002876*10000)}

C= 9.47 grams

And the remaining masss for t=1000 is:

y_{t=1000}= C e^{kt}

y_{t=1000}= 9.47 * e^{( -0.00002876*1000)}

y_{t=1000}= 9.20 grams

I hope it helps!

4 0
3 years ago
The cost of 4 cartons of fresh cream is $5.76. What is the cost of 13 such cartons? $16.25 $18.72 $18.76 $36.04
Natasha_Volkova [10]

Answer:

A

Step-by-step explanation:

8 0
3 years ago
18x=36 with a full explanation and I will give you brainlyest
iris [78.8K]

Answer:−18x>36

Divide both sides by −18. Since −18 is negative, the inequality direction is changed.

x< −18

36

​

Divide 36 by −18 to get −2.

x<−2

Step-by-step explanation:

Hope this helps!

5 0
2 years ago
What are the dimensions of a storage tank
motikmotik

Answer:

Step-by-step explanation:

550 48 6-0 3/16 3/16 800

1000 48 10-10 3/16 3/16 1300

1100 48 11-11 3/16 3/16 1400

1500 48 15-8 3/16 3/16 1650

65 9-0 3/16 3/16 1500

2000 65 11-10 3/16 3/16 2050

2500 65 14-10 3/16 3/16 2275

3000 65 17-8 3/16 3/16 2940

4000 65 23-8 3/16 3/16 3600

5000 72 23-8 1/4 1/4 5800

84 17-8 1/4 1/4 5400

7500 84 26-6 1/4 1/4 7150

96 19-8 1/4 1/4 6400

10000 96 26-6 1/4 5/16 8540

120 17-0 1/4 5/16 8100

12000 96 31-6 1/4 5/16 10500

120 20-8 1/4 5/16 9500

15000 108 31-6 5/16 5/16 13300

120 25-6 5/16 5/16 12150

20000 120 34-6 5/16 5/16 15500

25000 120 42-6 3/8 3/8 22300

30000 120 51-3 3/8 3/8 28000

4 0
2 years ago
A company that manufactures radios first pays a start-up cost, and then spends a certain amount of money to manufacture each rad
Tresset [83]

Answer:

5.25 represents the cost of each radio

Step-by-step explanation:

5 0
3 years ago
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