Question

The amount of carbon 14 still present is a sample after t years

Answer 1

Answer:

The age of this sample is 13,417 years.

Step-by-step explanation:

The amount of carbon 14 present in a sample after t years is given by the following equation:

$C(t) = C_{0}e^{-0.00012t}$

Estimate the age of a sample of wood discoverd by a arecheologist if the carbon level in the sampleis only 20% of it orginal carbon 14 level.

The problem asks us to find the value of t when

$C(t) = 0.2C_{0}$

So:

$C(t) = C_{0}e^{-0.00012t}$

$0.2C_{0} = C_{0}e^{-0.00012t}$

$e^{-0.00012t} = \frac{0.2C_{0}}{C_{0}}$

$e^{-0.00012t} = 0.2$

$ln e^{-0.00012t} = ln 0.2$

$-0.00012t = -1.61$

$0.00012t = 1.61$

$t = \frac{1.61}{0.00012}$

$t = 13,416.7$

The age of this sample is 13,417 years.