Question

A 15-gram sample of a substance that's a by-product of fireworks has a k-value of 0.1405. Find the substance's half-life, in days. Round to the nearest tenth.

Answer 1

"half life" is the amount of time it takes for a substance to lose 50% of it's mass

so we use our formula

y = a(e^kt) and plug in 7.5 for y, 15 for a, and 0.1405 for k

Answer 2

7.5 = 15 * e^(0.1405)t

dividing both sides by 7.5 gives us

0.5 = e^(0.1405t)

know where to go from here?

Answer 3

no idea lol i suck at this

Answer 4

in order to "eliminate" the e^( part we must take the natural log of both sides

ln(0.5) = lne^(0.1405t)

if we have ln(e^something) we can cross out the ln(e part

so we get

ln(0.5) = 0.1405t

then we simply divide both sides by 0.1405

Answer 5

I get 4.9 days

Answer 6

oh... im still so lost lol

Answer 7

that was right tho :D

Answer 8

well, let's take a closer look at our formula

Answer 9

y = a(e^-kt) *I forgot to put the negative sign before

Answer 10

this is the formula they give

Answer 11

ooh ok

Answer 12

since your problem gives you:

the initial mass
the final mass
and k, you can insert these into the formula and find t

Answer 13

wait whats the final mass?

Answer 14

since they are asking for "half-life" the final mass = initial mass/2

Answer 15

half-life is the amount of time it takes for the final mass to equal half the intial mass

Answer 16

i feel really dumb rn lol

Answer 17

don't worry about it, it's just a definition to memorize

Answer 18

wait than whats the 0 for?

Answer 19

the "0" is a subscript, it's just to make the N_0 different from the other N

Answer 20

oh ok

Answer 21

it's just a fancy label, it doesn't get treated like an actual 0

Answer 22

any other questions?

Answer 23

prob

Answer 24

i have another one can u like guide me through it?

Answer 25

sure, you can close this question and make a new one

Answer 26

cool