MATH SOLVE

3 months ago

Q:
# A student in Greece discovers a pottery bowlthat contains 21% of its original amount of C-14.N = Noe-ktNo = inital amount of C-14 (at time t = 0)N = amount of C-14 at timett = time, in yearsk = 0.0001age of the pottery bowl to the nearest year??

Accepted Solution

A:

Answer:The age of the pottery bowl to the nearest year is 15606 years.Step-by-step explanation:Let the initial amount of C-14 in the bowl i.e. [tex]N_{0} = 100[/tex] and today (say after t years) the amount of C-14 in the bowl i.e. N = 21.
Therefore, from the given equation we can write [tex]21 = 100 e^{- 0.0001t}[/tex] {Since, k is give to be 0.0001}
⇒ [tex]0.21 = e^{- 0.0001t}[/tex]
Now, taking ln on both sides we get
ln 0.21 = - 0.0001t (ln e) {Since, [tex]\ln a^{b} = b \ln a[/tex]}
⇒ - 1.560647 = - 0.0001t {We have ln e = 1}⇒ t = 15606.47 years ≈ 15606 years Therefore, the age of the pottery bowl to the nearest year is 15606 years.(Answer)