As we saw in Section 3.4, a radioactive substance decaysexponentially: The mass at time t  is  m(t) = m(0) ekt  , where m (0)is the initial mass and k is a negative constant. Themean life of M an atom in the substance is  M = -k integral 0 to infinity t e kt dtFor the radioactive carbon isotope,  14 C ?, used in radiocarbondating, the value of k is -0.000121 . Find the meanlife of a  14 C ? atom.

Q: 6. Show that the principal branch of the log function can be described by the formula log(z) = S 1/w…

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Q: The solution of 29 + 12 log3 (7 – 5x ) = 65 %3D -

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Q: 34.Half-life decay model is the time it takes for to half of its original quantity. It is denoted…

A: Half life decay formula is, At=A012td

Q: 1 a ae 9 = t"e 41 what value ofn will make %3D ar ar at -9 = log(x +y +z -3xyz), show that (x+y+z)*

A: Partial differential equations

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A: The quantity of plutonium after t years is Q=1812t24,100

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A: We have to use 1st order decay here.

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Q: (LO18) 24. The decay of 371mg of a radioactive substance is given by A(t) = 371 e - 0.018t where tis…

A: Given A(t) = 371 e-0.018t

Q: A(t) =

A: dAdt=0.05AA(t)=∫0.05Adt=0.05At

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.