A 14 gram sample of a substance thats used to sterilize surgical instruments has a k-value of 0.1481. find the substance half-life, in days

Question

A 14 gram sample of a substance thats used to sterilize surgical instruments has a k-value of 0.1481. find the substance half-life, in days round answer to the nearest tenth

in progress 0
Parker 7 months 2021-10-07T09:04:21+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-07T09:05:27+00:00

    Answer:

    The half life of the substance is [tex]\tau = 4.7 \:days[/tex].

    Step-by-step explanation:

    The equation that models the amount of substance after time [tex]t[/tex] is

    [tex]A = A _0 e^{-kt}[/tex].

    We are told that that the initial amount [tex]A_0= 14g[/tex], and the k-value is [tex]k = 0.1481[/tex]; therefore,

    [tex]A = 14e^{-0.1481t}[/tex]

    The half-life of the substance is the amount of time [tex]\tau[/tex] it takes to decay to half its initial value; therefore,

    [tex]\dfrac{A_0}{2} = A_0e^{-0.1481\tau }[/tex]

    [tex]e^{-0.1481\tau } = \dfrac{1}{2}.[/tex]

    Take the Natural Logarithm of both sides and get:

    [tex]ln[e^{-0.1481\tau } ]= ln[\dfrac{1}{2}][/tex]

    [tex]-0.1481\tau = ln[\dfrac{1}{2} ][/tex]

    [tex]\tau = \dfrac{ln[\dfrac{1}{2} ]}{-0.1481}[/tex]

    [tex]\boxed{\tau = 4.7 \:days}[/tex]

    Thus, we find that the half life of the substance is 4.7 days.

    0
    2021-10-07T09:05:59+00:00

    Answer:

    4.7

    Step-by-step explanation:

    I got 100% on my test.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )