Question

Situation:A farmer in China discovers a mammalhide that contains 57% of its originalamount of C-14.N = Noe-ktNo inital amount of C-14 (at time=t = 0)N= amount of C-14 at time tk= 0.0001t = time, in yearsFind the age of the mammal hide to the nearestyear.

Answer 1

Given:

A farmer in China discovers a mammal hide that contains 57% of its original

amount of C-14.

The given formula is

`N=N_0e^(-kt)`

where k =0.0001.

Required:

We need to find the age of the mammal hide.

Step-by-step explanation:

The number of mammals hiding is 57% of the original.

`N_t=57\text{ \%}`

We get

`\text{ We get }N_0=1\text{ and }N=57.`
`Substitute\text{ }N=0.57,\text{ }N_0=1\text{ and k=0.0001 in the equation }N=N_0e^(-kt)\text{ to find t value.}`
`0.57=1* e^(-0.0001t)`
`0.57=e^(-0.0001t)`

Take a natural log on both sides of the equation.

`In\text{ }0.57=Ine^(-0.0001t)`
`In\text{ }0.57=-0.0001* t`
`(-In0.57)/(0.0001)=t`
`5621.18=t`
`t=5621years.`

Final answer:

The age of the mammal hide is 5621 years.