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Vladimir79 [104]

3 years ago

10

Write a real-world problem that can be represented by a rule and a table using division

1 answer:

LuckyWell [14K]3 years ago

4 0

A company makes different size square containers. How can you find the length of each side if you know the perimeter of each of the containers? Represent your answer in a table, and right and equation that shows the rule used. You would write the equation x/4=y. I would create an input/output table with the labels x and y. I would then write various lengths for the perimeters and use the rule of dividing by 4 to find the y values.

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Read 2 more answers

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

6 0

3 years ago