Carbon-14 is a radioactive isotope that has a half-life of 5,730 years. Approximately how many years will it take for carbon-14 to decay to 10 percent of its original amount?

Carbon-14 will take 19,035 years to decay to 10 percent.

Step-by-step explanation:

Exponential Decay Function

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.

An exponential decay can be described by the following formula:

Where:

No  = The quantity of the substance that will decay.

N(t) = The quantity that still remains and has not yet decayed after a time t

    = The decay constant.

One important parameter related to radioactive decay is the half-life:

If we know the value of the half-life, we can calculate the decay constant:

Carbon-14 has a half-life of 5,730 years, thus:

The equation of the remaining quantity of Carbon-14 is:

We need to calculate the time required for the original amout to reach 10%, thus N(t)=0.10No

Simplifying:

Taking logarithms:

Solving for t:

Carbon-14 will take 19,035 years to decay to 10 percent.

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.

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )