Question

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

is given by the function C(t)=
Coe-.00012t
where co is the initial anong . estimate the age of a sample of
wood discoverd by a arecheologist if the carbon level in the sample
is only 20% of it orginal carbon 14 level.

Answer 1

The age of this sample is 13,417 years.

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) = (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 = (1.61)/(0.00012)`

`t = 13,416.7`

The age of this sample is 13,417 years.