Bones found in the Lascaux Caves in France have a carbon-14 disintegration rate of 2.25 disintegrations per minute per gram of carbon. If the rate of decay rate of carbon-14 at the time of death is 13.6 counts per minute per gram of carbon, calculate the age of the remnants. The half-life of carbon-14 is 5730 years.

14873 years

Step-by-step explanation:

The exponential decay of the ¹⁴C can be expressed as follows:

             (1)

where Nt: is the disintegration per minute per gram of carbon that has not yet decayed after a time t = 2.25, N₀: is the initial disintegration per minute per gram of carbon = 13.6 (at the time of death), λ: is the decay constant and t: is time.  

The half-life of carbon-14 is related to the decay constant by the following equation:

             (2)

Hence, by entering equation (2) into (1) we have:  

     (3)

Now, by solving equation (3) for t, we can find the age of the remnants:

Therefore, the age of the remnants is 14873 years.

I hope it helps you!            

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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