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2 years ago

Please help! will give brainliest if right

Mathematics

2 answers:

asambeis [7]2 years ago

7 0

Answer:

first option

Step-by-step explanation:

y = 1/4x - 5/4

this line has a slope of 1/4 and a y-intercept of -5/4

steposvetlana [31]2 years ago

7 0

Answer:

First opnion is correct

Step-by-step explanation:

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Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 3%. If the rate of deca

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Answer:

The half-life of the radioactive substance is 135.9 hours.

Step-by-step explanation:

The rate of decay is proportional to the amount of the substance present at time t

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$\frac{dQ}{dt} = -rt$

Which has the following solution:

$Q(t) = Q(0)e^{-rt}$

In which Q(t) is the amount after t hours, Q(0) is the initial amount and r is the decay rate.

After 6 hours the mass had decreased by 3%.

This means that $Q(6) = (1-0.03)Q(0) = 0.97Q(0)$ . We use this to find r.

$Q(t) = Q(0)e^{-rt}$

$0.97Q(0) = Q(0)e^{-6r}$

$e^{-6r} = 0.97$

$\ln{e^{-6r}} = \ln{0.97}$

$-6r = \ln{0.97}$

$r = -\frac{\ln{0.97}}{6}$

$r = 0.0051$

$Q(t) = Q(0)e^{-0.0051t}$

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This is t for which Q(t) = 0.5Q(0). So

$Q(t) = Q(0)e^{-0.0051t}$

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$e^{-0.0051t} = 0.5$

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$-0.0051t = \ln{0.5}$

$t = -\frac{\ln{0.5}}{0.0051}$

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