Question

If you have 10.0 g of a substance that decays with a half-life of 14 days, then how much will you have after 42 days?

A. 0.10 g

B. 0.31 g

C. 1.25 g

D. 2.50 g

Answer 1

here we have to apply this formula:
\[\Large m\left( t \right) = {m_0}{e^{ - t/\tau }}\]
where m_0 is the initial mass of our sample, m(t) is the mass of our sample at time t, and \tau is the half life

Answer 2

ok! what do we plug in?

Answer 3

here is the next step:
\[\Large m\left( {42} \right) = 10 \times {e^{ - 42/14}} = \frac{{10}}{{{e^3}}} = ...grams\]

Answer 4

ok! what is e?

Answer 5

oh wait sorry haha i totally blanked out :P

Answer 6

we get 0.497870684?

Answer 7

e is the Neperus constant, namely:
\[e = 2.71828\]

Answer 8

yes:)

Answer 9

yes! I got 0.49

Answer 10

my formula is the correct one!

Answer 11

yay!! what would the solution be though? 0.49 is not a choice :/

Answer 12

please wait, I'm checking my computation

Answer 13

ok!

Answer 14

I think that
\[\tau \] is the average life, and it is given by the subsequent formula:
\[\tau = \frac{{14}}{{0.693}} = 20.2\;days\]

Answer 15

ohh okay! i am confused, though... which choice would be the accurate solution? :/

Answer 16

so the right answer is given by the subsequent computation:
\[\Large m\left( {42} \right) = 10 \times {e^{ - 42/20.2}} = \frac{{10}}{{{e^{2.079}}}} = ...grams\]

Answer 17

oh! ok! so we get 1.25! so choice C is the solution?

Answer 18

yes! that's right!

Answer 19

yay! thank you!!:) okay! onto the next:)

Answer 20

:) ok!