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 .y=yoe−0.00012t. The paint contains 1414​% of its​ carbon-14. How old are the​ paintings?

Answer 1

Answer:

16,383.33 years ( approx )

Step-by-step explanation:

Given equation that shows the amount of carbon-14 after t years,

$y = y_0 e^{-0.00012t}$

Where,

$y_0$ = initial amount,

∵ 14% of $y_0$ = $\frac{14}{100}y_0$ = $\frac{7}{50}y_0$

$\frac{7}{50}y_0= y_0 e^{-0.00012t}$

$\frac{7}{50}=e^{-0.00012t}$

Taking ln both sides,

$\ln(\frac{7}{50})=-0.00012t$

$-1.966=-0.00012t$

$\implies t =\frac{-1.966}{-0.00012}=16383.33$

Hence, the painting would be 16383.33 years old ( approx )