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arsen [322]
2 years ago
14

The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.

3 hours. If 1 gram of this isotope is present initially, how long will it take for 70% of the lead to decay? (Round your answer to two decimal places.)
Mathematics
1 answer:
Ksenya-84 [330]2 years ago
5 0

Answer:

5.73 hours

Step-by-step explanation:

70% decay means 30% remains

.3 = (1/2)^(t/3.3)

take the log of both sides

log.3 = t/3.3 * log1/2

Divide both sides by log 1/2

log.3 / log1/2 = t/3.3

use calculator

1.736965594166206 = t/3.3

multiply both sides by 3.3

5.73198646074848 = t

rounded

t = 5.73 hours

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Which expression has the same value as 37.4 - 54.9?
GrogVix [38]

Answer:

D

Step-by-step explanation:

In the original expression =  37.4 - 54.9 = -17.5

So, we have to solve all the equations but 1 of them has to equal to -17.5

A) -54.9 + (-37.4) = -92.3

   Remove parentheses

   = -54.9 - 37.4

Subtract the numbers

    -92.3

B) 54.9 - 37.4 = 17.5

Since 54.9 is greater than 37.4 just subtract normally

 4   14

  5  4.   9                < ------- Line up the decimal points like this

-  3  7.   4                <---------  Subtract the decimals

-----------------

   1   7   .    5       <---------- This is the final answer to B.                    

 

C)  37.4 - (- 54.9) = 92.3

   Change the sign to addition

        =37.4 + 54.9

  Add the numbers normally

  54.9

+ 37. 4

--------------

  92.3

D)  37.4 + (-54.9) = -17.5

   Change the sign to subtraction

      =    37.4 - 54.9

Subtract them normally (but as you can see you are subtracting a smaller number from a larger number so heres a trick that you can use switch the equation by putting the larger number in first like this....)

54.9 - 37.4 = 17.5 (REMEMBER the answer is not 17.5 because the original equation of D is reversed  37.4 - 54.9 so in this case your answer should be

- 17.5)

37.4 - 54.9 = -17.5

Your final answer is D because it matches 37.4 - 54.9.

Hope this helps!

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