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Orlov [11]
3 years ago
15

Cesium-137 has a half-life of about 30 years. A) Find the annual decay rate and round final result to 4 decimal places. B) Find

the continuous decay rate and round final result to 4 decimal places. C) How long will it take for a 10 gram sample to decay to 1 gram? Round to nearest year and interpret your result with a complete sentence. D) Complete this statement: as x goes to infinity, y goes to ___.
Mathematics
1 answer:
MrMuchimi3 years ago
8 0

Answer:

  • 0.0228
  • 0.0231
  • 100 years
  • 0

Step-by-step explanation:

The exponential equation for the fraction remaining after x years can be written as ...

  y = (1/2)^(x/30)

A) For x=1, the fraction remaining is ...

  y = (1/2)^(1/30) ≈ 0.97716 = 1 - 0.0228

Of the original amount, 0.0228 decays each year.

__

B) The continuous decay rate is the natural log of the growth factor, so is ...

  ln(0.97716) = -0.0231

The continuous decay rate is 0.0231 of the present amount (per year).

__

C) For y=.10 (1/10 of the original amount) we find x to be ...

  .1 = .5^(x/30)

  ln(.1) = (x/30)ln(.5) . . . . . take the natural log

  30ln(0.1)/ln(0.5) = x ≈ 100 . . . years

It will take 100 years for a 10-gram sample to decay to 1 gram.

__

D) As x goes to infinity, y goes to zero.

_____

The relationship between growth rate and growth factor is ...

  growth factor = 1 + growth rate

When the growth rate is negative, it is called a decay rate.

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EASY 7TH GRADE MATH, WILL GIVE BRAINLIEST AND THANKS
Fudgin [204]

Answer:

D. 8

Step-by-step explanation:

2p=16

divide both sides by 2 to get p alone

p=8

7 0
2 years ago
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Carissa counts by 5s from 32 to 62. Which number does carissa count?
polet [3.4K]

Answer:

32, 37, 42, 47, 52, 57, 62.

Step-by-step explanation:

It is given that Carissa counts by 5s from 32 to 62.

It means, we have to add 5 in the number to get the next number.

Add 5 in 32.

32+5=37

Now, add 5 in 37.

37+5=42

Similarly, continue the process.

42+5=47

47+5=52

52+5=57

57+5=62

Therefore, the numbers counted by carissa are 32, 37, 42, 47, 52, 57, 62.

8 0
3 years ago
Gerardo has just invested in a bond worth $470 that is expected to increase in value by 6% per year. Write the equation used to
Viefleur [7K]

Answer:

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $470

r = 6% = 6/100 = 0.06

n = 1 because it was compounded once in a year.

Therefore, the equation used to determine the value of his bond after t years is

A = 470(1 + 0.06/1)^1 × t

A = 470(1.06)^t

3 0
3 years ago
in a five character password the first two characters must be digits and the last three characters must be letters if no charact
Vilka [71]

Answer:

1,404,000 unique passwords are possible.

Step-by-step explanation:

The order in which the letters and the digits are is important(AB is a different password than BA), which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

P_{(n,x)} = \frac{n!}{(n-x)!}

In this question:

2 digits from a set of 10(there are 10 possible digits, 0-9).

3 characters from a set of 26. So

P_{10,2}P_{26,3} = \frac{10!}{8!} \times \frac{26!}{23!} = 10*9*26*25*24 = 1404000

1,404,000 unique passwords are possible.

5 0
3 years ago
.98345 × 100 = ? A. 983.45 B. 9.8345 C. .0098345 D. 98.345
Alexxx [7]
When you multiply by 100, you move the decimal point two places to the left so 0.98345 becomes 98.345.

Option D)
3 0
3 years ago
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