Answer:
m(t) = m₀ e⁻⁰•⁰¹⁵ᵗ
Half-Life = 46.21 years.
Step-by-step explanation:
Radioactive reactions always follow a first order reaction dynamic
Let the initial mass of radioactive substance be m₀ and the mass at any time be m
(dm/dt) = -Km (Minus sign because it's a rate of reduction)
The question provides K = 0.015 from the given differential equation
(dm/dt) = -0.015m
(dm/m) = -0.015dt
∫ (dm/m) = -0.015 ∫ dt
Solving the two sides as definite integrals by integrating the left hand side from m₀ to m and the Right hand side from 0 to t.
We obtain
In (m/m₀) = -0.015t
(m/m₀) = (e^(-0.015t))
m = m₀ e^(-0.015t)) = m₀ e⁻⁰•⁰¹⁵ᵗ
m(t) = m₀ e⁻⁰•⁰¹⁵ᵗ
At half life, m(t) = (m₀/2), t = T(1/2)
(m₀/2) = = m₀ e⁻⁰•⁰¹⁵ᵗ
e⁻⁰•⁰¹⁵ᵗ = (1/2)
In e⁻⁰•⁰¹⁵ᵗ = In (1/2)
-0.015t = - In 2
t = (In 2)/0.015
t = (0.693/0.015)
t = 46.21 years
Half life = T(1/2) = t = 46.21 years.
Hope this Helps!!!
1/2p-2=x would be your equation <span />
Answer:
2x-3 < 7 = x ≤ 5 and 5 - x ≤ 8 = x ≥ - 3
Step-by-step explanation:
Answer:
standard form is Ax + by + c = 0
Step-by-step explanation:
add 5x to each side to get 5x + y - 2 = 0
Jasmine is running faster.
Since the track is 1/5 of a km and she can run 1km in 7 minutes, divide seven to get 1.4.
This means that Jasmine can run one lap in 1.4 minutes.
Since a Kyah can run 6 laps in 10 minutes, do 10 divided by 6 and the answe will be 1.6 repeating.
1.4 < 1.6 so Jasmine is faster