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3 years ago

Find a substance half-life in days. round your answer to the nearest tenths

Mathematics

2 answers:

Rus_ich [418]3 years ago

7 0

Answer:

t=6.2days

Step-by-step explanation:

Find a substance half-life in days. round your answer to the nearest tenths

k value=0.1124

N0=33 grams

since the questions says the time it takes for the substance to reduce to half of its size. the initial mass doesn't matter

N=N0e^-kt

N/N0=e^-kt

take laperian log of both sides

Ln(N/N0)=-kt

Ln(0.5)=-0.1124t

-0.693=-0.1124t

t=6.16

t=6.2days

Note: Half life is the time it takes for a radioactive material to reduce to half of its size/mass.

jeka57 [31]3 years ago

3 0

A 33 gram sample has k value of .1124
(Actually I think the problem SHOULD be worded: A 33 gram sample has k value of -.1124/days)

See attached graphic:
Half-Life = ln (.5) / k
Half-Life = -.693147 / -.1124/days
Half-Life = <span> <span> <span> 6.1667882562 </span> </span> </span> days

Source:
http://www.1728.org/halflif2.htm

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Step-by-step explanation:

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$x=\frac{-(-151)\frac{+}{} \sqrt{151^2-4*1*1575} }{2*1}$

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$x=\frac{-(-151)+128.45}{2} \\\\\x=\frac{279.45}{2} \\\\x=139.72 \\\\\\x=\frac{-(-151)-128.45}{2}\\\\x=\frac{151-128.45}{2}\\\\x=\frac{22.55}{2}\\\\x=11.27$

the first answer x= 139.72 approximately 140 minutes mins is correct for Bobby's time

let us check

$\frac{63}{140}+\frac{63}{140-25}=1\\\\\\0.45+\frac{63}{115} =1\\\\0.45+0.5478=1\\0.997 =1$

we can see that the solution approximates to 1

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