Question

The radioactive substance strontium -90 has a half-life of 28 years. In other words, it takes 28 years for half of a given quantity of strontium -90 to decay to a non radioactive substance. The amount of radioactive strontium -90 still present after t years is modeled by the expression 80*2^-t/28 grams. Evaluate the expression for t=0, t=28, and t=56. What does each value of the expression represent?

Answer 1

First of all the half life is the amount of time it takes for a substance to decay to half of its original amount. \[80\times2^{-t/28}\] All you need to do is plug in t=0, t=28 and t=56. Then what does it mean when we evaluated at time zero? how about after 28 years? after 56?

Answer 2

how do you plug it in cause iv never did this b4

Answer 3

Solving for zero we just replace t with zero which gives\[80\times2^{-\frac{ -(0) }{ 28 }}\] which simplifies to \[80\times2^{0}\]
and number to the power 0 is 1. So we have \[80\times1=80\]
What does this mean? After no time has passed we have 80 units of this strontium 90

Answer 4

do you have a calculator that can calculate exponents?

Answer 5

I have no clue this is my first time seeing a question like this

Answer 6

What kind of calculator do you have?

Answer 7

i think its a scientific one

Answer 8

ok good. Do you see the button that looks like this\[x ^{y} \] or ^

Answer 9

yes

Answer 10

k thats the button that does exponents. so to evaluate at t=28 your going to plug into your calculator kind of like this:
80 X 2^(-28/28)

Answer 11

you should get 40

Answer 12

cause 2^(-28/28) is 2^(-1) which is 1/2 and 80 X 1/2= 40

Answer 13

yep thats what i got

Answer 14

good now try for t=56 and see what you get

Answer 15

so instead of 28 put 56?

Answer 16

yup

Answer 17

ok hold on

Answer 18

its 40 also?

Answer 19

make sure you only plug in 56 for t. so 80X2^(-t/28) will be 80X2^(-56/28)

Answer 20

oh ok i put 56 twice instead of 28 hold on

Answer 21

its 20

Answer 22

yup now you just need to think about what each value represents

Answer 23

ok umm how do you do that lol sorry im a little slow :)

Answer 24

so at t=0 that means no time has passed and we have 80 units of the substance so 80 is our original amount.
at t=28 one half life has passed because the half life of theis substance in 28 years so at t=28 half of the original amount is present. 40 right?
then at t=56 two half lives have passed because 28+28=56 and so 1/2*1/2=1/4 so we should have 1/4 of the original amount and we saw that at t=56 there were 20 units of the original amount. and 80X(1/4)=20.

Answer 25

so the value that they represent is 20?

Answer 26

each time value (t=0, t=28 and t=56) represents something different.
t=0 is the original amount
t=28 is half of the original amount
and t=56 is half of half of the original amount

Answer 27

oh ok thank you so much @Mr.Me