Question

The amount of​ carbon-14 present in a paint after t years is given by y equals y Subscript o Baseline e Superscript negative 0.00012 t Baseline . The paint contains 27​% of its​ carbon-14. How old are the​ paintings?

Answer 1

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

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

=>    $0.27 = * e ^{-0.00012t}$

=>    $ln(0.27) = -0.00012t$

=>  $- 1.30933 = -0.00012t$

=>  $t = \frac{-1.30933}{-0.00012}$

=>   $t = 10911.1 \ years$