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Anettt [7]
3 years ago
6

A population of 1200 leopards decreases by 12% per year. How many leopards will there be in the population after 6 years? Round

your answer to the nearest whole number
Mathematics
1 answer:
frez [133]3 years ago
3 0
12% of 1200 is 144, so subtract that. you get 1056. 12% of that is 126.72, so you subtract that. you get 929.28. 12% of that is 111.5136 and you subtract that. and so on and so forth. the answer would be 557.
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Element X decays radioactively with a half life of 12 minutes. If there are 200 grams of Element X, how long, to the nearest ten
Semenov [28]

Answer:

It would take 24 minutes for the element to decay to 50 grams

Step-by-step explanation:

The equation for the amount of the element present, after t minutes, is:

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

In which Q(X) decays radioactively with a half life of 12 minutes.(0) is the initial amount and r is the rate it decreases.

Half life of 12 minutes

This means that Q(12) = 0.5Q(0)

So

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

0.5Q(0) = Q(0)e^{-12r}

e^{-12r} = 0.5

\ln{e^{-12r}} = \ln{0.5}

-12r = \ln{0.5}

12r = -\ln{0.5}

r = -\frac{\ln{0.5}}{12}

r = 0.05776

If there are 200 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 50 grams?

This is t when Q(t) = 50. Q(0) = 200.

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

50 = 200e^{-0.05776t}

e^{-0.05776t} = 0.25

\ln{e^{-0.05776t}} = \ln{0.25}

-0.05776t = \ln{0.25}

0.05776t = -\ln{0.25}

t = -\frac{\ln{0.25}}{0.05776}

t = 24

It would take 24 minutes for the element to decay to 50 grams

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4 years ago
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