Mathematics, 22.11.2019 23:31 toxsicity

The function q(t)=qoe^kt may be used to model radioactive decay. q representing the quantity remaining after t years; k is the decay constant. what is the decay constant for plutonium -240 if it's half-life is 6,300 years?

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Answer from: floresvanexel4pejp1p

A. -[ln(0.5)/6,300]

Step-by-step explanation:

Done on apex, it is correct.

Answer from: tjaigirl

Answer : The value of decay constant is, $1.1\times 10^{-4}\text{ years}^{-1}$

Explanation :

Half-life of plutonium-240 = 6300 years

The expression used to calculate the rate constant is:

$k=\frac{0.693}{t_{1/2}}$

where,

k = decay constant

$t_{1/2}$ = half-life

Now put all the given values in the above formula, we get:

$k=\frac{0.693}{6300\text{ years}}$

$k=1.1\times 10^{-4}\text{ years}^{-1}$

Therefore, the value of decay constant is, $1.1\times 10^{-4}\text{ years}^{-1}$

Answer from: Quest

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

Me if you can and if you finished this lesson on edg- comment you.

Answer from: Quest

The right of a lender to refuse a loan if the borrower hasn't repaid previous loans on time

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The function q(t)=qoe^kt may be used to model radioactive decay. q representing the quantity remaini...

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