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Fittoniya [83]
3 years ago
10

The amount of​ carbon-14 present in a paint after t years is given by y equals y Subscript o Baseline e Superscript negative 0.0

0012 t Baseline . The paint contains 27​% of its​ carbon-14. How old are the​ paintings?
Mathematics
1 answer:
sesenic [268]3 years ago
5 0

Answer:

The painting is t =  10911.1 \ years \ old

Step-by-step explanation:

From the question we are told that

    The amount of carbon present after t year is

           y(t) =  y_o * e ^{-0.00012t}    {Note ; This is the function }

Here  y(t) is the amount of carbon-14 after time t

        y_o the original amount of carbon-14

Now given that the paint as at now contain 27% of the original carbon-14

  Then it mean that

            y(t) =  0.27 y_o

So the equation is represented as

       0.27 y_o  =  y_o * e ^{-0.00012t}

=>    0.27  =  * e ^{-0.00012t}

=>    ln(0.27)   =   -0.00012t

=>  - 1.30933  =   -0.00012t

=>  t  =  \frac{-1.30933}{-0.00012}

=>   t =  10911.1 \ years

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