Respuesta :
Answer:
a) $15,406,443
b) 279.04 years = 279 years.
c) 5246.9 years = 5247 years.
Step-by-step explanation:
Compound interest
The final amount obtainable, A, from saving an initial amount, P, compounded at a rate of r in t number of years is given as
A = P (1 + r)ᵗ
A = ?
P = $100
r = 6% = 0.06
t = 2005 - 1800 = 205
A = 100 (1 + 0.06)²⁰⁵ = 100 × 154064.43 = $15406443
b) Radioactivity
Let the initial amount of Strontium be A
After 1 half life,
Amount remaining is A/2
After two half lives,
Amount remaining = A/2²
After 3 half lives,
Amount remaining = A/2³
After n half lives,
Amount remaining = A/2ⁿ
So, for this question,
(A)/(A/2ⁿ) = 1000
2ⁿ = 1000
In 2ⁿ = In 1000
n = (In 1000)/(In 2)
n = 9.966
1 half life = 28 years
n half lives = n × 28 = 9.966 × 28 = 279.04 years.
c) Carbon dating
The general relation of amount left to amount of Carbon-14 that is started with follows a first order rate of decay kinetics like every radioactive decay
A = A₀ e⁻ᵏᵗ
A = amount of Carbon-14 left at any time
A₀ = initial amount of Carbon-14
k = rate constant = (In 2)/(half life) = 0.693/5730 = 0.000121 /year.
(A/A₀) = 53% = 0.53
e⁻ᵏᵗ = 0.53
-kt = In 0.53 = -0.6349
t = 0.6349/k = 0.6349/0.000121 = 5246.9 years = 5247 years
