Question

I need help with
The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.

Answer 1

The general form is N(t)/N(0) = exp(-kt)

N(t) is the amount (mass, number) of radioactive atoms at time t.

Get k by knowing one such ratio.Here, the half-life is 32 days,

N(32)/N(0) = 0.5 = exp(-32 k)

ln (0.5) = - 0.693 = - 32 k

k = 0.0217 / day.

Put this k into exp(-kt) with t = 5 days and now have
fraction left. (nearly 90%)

Multiply fraction left by original mass and get final mass.

Answer 2

this is the one I don't understand I picked A which was wrong

Answer 3

so what is the final mass

Answer 4

can someone help me

Answer 5

The equation I use for this problem is m(t)= Ce^kt

\[180.5=361e ^{32k}\]
\[\frac{ 180.5}{ 361 } = e ^{32k}\]
\[\ln \frac{ 1 }{ 2}= \ln e ^{32k}\]
\[\ln \frac{ 1 }{ 2 }= 32k\]
\[\frac{ 1 }{ 32}\ln \frac{ 1 }{ 2 }= k\]

m(t)= \[361e ^{1/32\ln(1/2) t}\]
That's your equation. then you plug in your time t=5 to find how much material remains.

Answer 6

I don't have a calculator on hand right now

Answer 7

323.945