Mathematics, 03.10.2019 01:30 marshalldayton1452

Ancient paintings were found on cave walls in south america. the carbon-14 in the paintings was measured and was found to be 19% of the original weight. how old were the paintings?

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Answer from: leapfroggiez

Painting is 13725 years old.

Step-by-step explanation:

C-14 dating is the process through which age of fossils or dead tissues are determined.

One important thing about the C-14 dating is half life life period of C-14 that is 5730 years.

Now we know for C-14 decay we use the formula

$A_{t}=A_{0}e^{-kt}$

where $A_{t}$ = present quantity of C-14

$A_{0}$ = Initial quantity of C-14

k = Decay constant

t = Duration or time

We will calculate the decay constant first to use this formula for age determination further.

For Half life of C-14

A_{t}=A_{0}e^{-kt}

$\frac{1}{2}=1.e^{-k(5730)}$

Taking ln on both the sides

$ln(\frac{1}{2})=ln(1.e^{-k(5730)})$

-ln2=-5730k(lne)

k = $\frac{ln2}{5730}=(1.21)(10)^{-4}$

Now we have been given in the question that C-14 found to be 19% and we have to determine the age of the painting.

$A_{t}=A_{0}e^{-kt}$

$0.19=1\times (e^{-(1.21\times 10^{-4})t})$

We will take ln on both the sides

$ln(0.19)=ln[1\times (e^{-(1.21\times 10^{-4})t})]$

$-1.6607=-(1.21\times 10^{-4})t\times lne$

$t=\frac{1.6607}{1.21\times 10^{-4}}$

t = 1.3725× $10^{4}$

t = 13725 years

Therefore, painting is 13725 years old.

Answer from: lodridge

13713.717 years

Step-by-step explanation:

The exponential decay model for Carbon-14 is modeled by the following formula:

$A=A_{0}\;e^{-0.0001211\;t}$

where:

A_0 is the initial amount of Carbon-14

A is the final amount of Carbon-14, $A = 0.19 \times A_0$

t is the elapsed time in years since the painting was made

Replacing in the formula:

$0.19 \times A_0=A_{0}\;e^{-0.0001211\;t}$

$0.19=e^{-0.0001211\;t}$

$ln(0.19)=-0.0001211\;t$

$\frac{ln(0.19)}{-0.0001211}=t$

13713.717 years=t

Answer from: Quest

Best answer that i found on yahoo ok set : x= length of 2nd piece in cm x- 3= length of 1st piece in cm x-4= length of 3rd piece in cm then since you know they all came from the 20 cm ribbon you add them together and set them equal to 20x+ x-3 +x-4 = 20 3x - 7= 20 3x= 27 x= 9 the shortest piece is the third piece which is x- 4 x-4 9-4 = 5 the length of the smallest piece is 5 cm. the other lengths are 9 cm 6 cm

Answer from: Quest

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the x-axis .

step-by-step explanation:

Which of the following statements best describes the transverse axis of a hyperbola?

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Ancient paintings were found on cave walls in south america. the carbon-14 in the paintings was meas...