The amount of carbon-14 ( _6^14text(C)) in a wooden artifact is measured to be 12.5 percent the amount in a fresh sample of wood from the same region. The half-life of carbon-14 is 5715 years. Assuming the same amount of carbon-14 was initially present in the artifact, determine the age of the artifact.

17145 years

Step-by-step explanation:

Let n be the quantity of carbon-14 in the wooden artifact and n₀ be the quantity in the fresh sample of wood. The percentage of carbon -14 in the wooden artifact = 12.5%. This implies that n/n₀ = 12.5/100 = 0.125

For the carbon-14 to decay to 12.5% of its original value, it takes

(1/2)ⁿ have lives  which equals 0.125

(1/2)ⁿ = 0.125 = 125/1000 = 1/8 = 1/2³

So, n = 3. It becomes 12.5% after three half lives.

So the original age of the artifact = 3 × half - life = 3 × 5715 = 17145 years

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1