Question

A 45 gram sample of a substance that's used to sterilize surgical instruments has a k-value of 0.15
Formula: N=N0e^-kt
Find the substance's half-life, in days. Round to nearest tenth.

Answer 1

we can solve for t then plug in the numbers

Answer 2

\[N = N_{0}e^{-kt}\]

\[\frac{ N }{ N_{0} } = e^{-kt}\]

\[Ln(\frac{ N }{ N_{0} }) = Ln(e^{-kt})\]

\[Ln(\frac{ N }{ N_{0} }) = -kt \]

so this is how you would isolate t

\[\frac{ Ln(\frac{ N }{ N_{0} }) }{ -k } = t \]

now, all you need to do is to plug in your values.

N0 would be 45

so N would be half of that 22.5

Answer 3

take a look at the math, you notice that you first solve for the variable you're looking for then plug in the numbers afterwards.

Answer 4

I'm not good at this stuff :/ I'm really confused

Answer 5

So here is the formula re-arranged for the variable that we want to find

\[Ln(\frac{ N }{ N_{0} })*k^{-1} = t \]

Answer 6

\[N = our~final~ample \]

\[N_{0} = our~initial~mass\]

Answer 7

I never actually learned this stuff properly so that's why I'm really confused, I just switched to online classes

Answer 8

do you know what half life is?

Answer 9

half of a number? (guess)

Answer 10

it is the time, it takes for half of our sample to go away

Answer 11

okay still confused

Answer 12

I have 20 more questions and it's 1 am fml

Answer 13

so let's say if I have 50 grams of a sample right? and it takes 20 minutes to get to 25

what can you conclude form this?

Answer 14

it decreaes?

Answer 15

yes but it decreases by half

Answer 16

so the time it takes for the sample to decrease by half is called the half life.

Answer 17

okay