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Elenna [48]
3 years ago
7

Ok maths experts ,here is your trigonometric question

Mathematics
1 answer:
EleoNora [17]3 years ago
6 0

Answer:


Step-by-step explanation:

i don't take trig :/

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It is known that the mass, m(t), of a radio-active substance decreases as it decays, and that the equation governing this is m′(
Murljashka [212]

Answer:

m(t) = m₀ e⁻⁰•⁰¹⁵ᵗ

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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

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The question provides K = 0.015 from the given differential equation

(dm/dt) = -0.015m

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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

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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

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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!!!

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