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Fiesta28 [93]
3 years ago
11

A scientist left a 32-gram sample of a radioactive substance out and it was exposed to the air. After 30 minutes, only 26 grams

remained.
How much was left when the janitor found it 8 hours after the scientist left?
What is the half-life of this substance?
Hey, can anyone help me solve this. I'm not sure i'm answering it correctly.Thank you.
Mathematics
1 answer:
crimeas [40]3 years ago
4 0

Answer:

There were 1.155 g of the substance eight hours later and it's halflife time is 1.66943 h.

Step-by-step explanation:

Since radiactive decay is expressed by a exponential function of the following kind:

mass(t) = mass(0)*e^(-a*t)

Where mass(t) is the mass of the substance at a given time, mass(0) is the inital mass substance, a is a factor that defines how fast the substance will decay and t is the elapsed time. The problem provided us with all the needed information to create the expression, with the exception of the "a". So we can apply it to the known point in order to determine "a". We have:

mass(0.5) = 32*e^(-a*0.5)

26 = 32*e^(-a*0.5)

e^(-0.5*a) = 26 / 32

e^(-0.5*a) = 0.8125

ln[e^(-0.5*a)] = ln(0.8125)

-0.5*a*ln(e) = ln(0.8125)

-0.5*a = ln(0.8125)

a = -ln(0.8125)/0.5 = 0.4152

So the expression that represents the mass of the substance over time is given by:

mass(t) = 32*e^(-0.4152*t)

After 8 hours we have:

mass(8) = 32*e^(-0.4152*8) = 32*e^(-3.3216) = 1.155 g

The half life is the time it'll take to reach half it's original mass, therefore:

16 = 32*e^(-0.4152*t)

32*e^(-0.4152*t) = 16

e^(-0.4152*t) = 16 / 32

e^(-0.4152*t) = 0.5

ln[e^(-0.4152*t)] = ln(0.5)

-0.4152*t = ln(0.5)

t = -ln(0.5)/0.4152 = 1.66943 h

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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7 0
2 years ago
The altitude a ( in feet) of a plane t minutes after lift off is given by a=3400t+600
Julli [10]

Answer:

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Step-by-step explanation:

'a' in the formula represents altitude in feet. You are told the altitude is 21000 feet, so put that into the formula:

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  6 = t . . . . . . . . . . . . . . . divide both sides by 3400

The problem statement tells you that t represents minutes after lift off, so this solution means the altitude is 21000 feet 6 minutes after lift off.

The question is asking for the number of minutes after lift off that the plane reaches an altitude of 21000 feet, so this answers the question directly:

  The plane is at an altitude of 21000 feet 6 minutes after lift off.

4 0
2 years ago
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rodikova [14]

Answer:

Then the total area is  116 cm^2 which agrees with answer D

Step-by-step explanation:

Notice we need to calculate the area of two rectangles (one larger at the bottom and a smaller one on top)

The Area of a rectangle is the product: base x height

In our case :

Area of Big rectangle = 12 cm x 7 cm = 84 cm^2

Area of smaller rectangle = 8 cm x 4 cm = 32 cm^2

Then the total area is: 84 cm^2 + 32 cm^2 = 116 cm^2

8 0
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Percentage of a number.

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4 0
3 years ago
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