Question

Situation:
A student in Greece discovers a pottery
bowl that contains 65% of its original
amount of C-14.
N = Noe-kt
No inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Find the age of the pottery bowl to the nearest
year.
Enter the correct answer.
000
?
DONE

Answer 1

The age of the pottery bowl to the nearest year is 4307 years. Using exponential decay or growth formula, the required value is calculated.

What is the formula for exponential growth/decay?

The formula for the exponential growth/decay is

$N=N_0e^-^k^t$

Where,

N - the total amount after time t

N₀ - the initial amount

k - growth or decay rate

t - time

Calculation:

It is given that,

A student in Greece discovers a pottery bowl that contains 65% of its original amount of C-14.

⇒ N(t) = 0.65N₀

But we have k = 0.0001.

Then,

$N(t)=N_0e^-^k^t$

0.65 N₀ = N₀ $e^{-(0.0001)t}$

⇒ 0.65 = $e^{-(0.0001)t}$

⇒ ln $e^{-(0.0001)t}$ = ln 0.65

⇒ -(0.0001)t = -0.4307

⇒ t = 0.4037/0.0001

∴ t = 4307 years.

Thus, the age of the pottery bowl is 4307 years.

Learn more about exponential growth or decay here:

https://brainly.com/question/1979778

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