a 10 gram sample of a substance that's used to detect explosives has k-value of 0.1353, find the substance half life in days, Ro

Question

crimeas [40]

3 years ago

6

a 10 gram sample of a substance that's used to detect explosives has k-value of 0.1353, find the substance half life in days, Ro

und your answer to the nearest hundreth

Mathematics

2 answers:

olchik [2.2K] · Answer 1 · 2022-02-14T04:25:15+03:00

olchik [2.2K]3 years ago

5 0

5.1 is the correct answer.

IrinaK [193] · Answer 2 · 2022-02-14T02:10:35+03:00

We find the value of N₀ since we are provided with initial conditions.
The condition is that, at time t = 0, the amount of substance contains originally 10 grams.
We substitute:
10 = N₀ (e^(-0.1356)*0)
10 = N₀ (e^0)
N₀ = 10

When the substance is in half-life (meaning, the half of the original amount), it contains 5 grams. We solve t in this case.
5 = 10 e^(-0.1356*t)
0.5 = e^(-0.1356*t)
Multiply natural logarithms on both sides to bring down t.
ln(0.5) = -0.1356*t
Hence,
t = -(ln(0.5))/0.1356
t ≈ 5.11 days (ANSWER)