Question

Can someone help me with this, please? I really need help!

Strontium-90 (Sr-90) has a half-life of approximately 29 years. Let the initial amount of Sr-90 in a sample be 100g. If the decay function s(y)=100*0.5^y/29 expresses the amount of Sr-90 that remains in the sample after y years, in how many years will 1g of Sr-90 be left? Round up your answer to the nearest number of years

Answer 1

Answer: Approximately 193 years

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Work Shown:

y = number of years

s(y) = amount of Strontium-90 (Sr-90) in grams

We plug in s(y) = 1 and solve for y to determine how long it takes for the initial 100 gram sample to decay to 1 gram.

s(y)=100*0.5^(y/29)

1=100*0.5^(y/29)

1/100 = 0.5^(y/29)

0.01 = 0.5^(y/29)

Log[ 0.01 ] = Log[ 0.5^(y/29) ] .... see note1 below

Log[ 0.01 ] = (y/29)*Log[ 0.5 ] .... see note2

(y/29)*Log[ 0.5 ] = Log[ 0.01 ]

y/29 = Log[ 0.01 ]/Log[ 0.5 ]

y = 29*Log[ 0.01 ]/Log[ 0.5 ]

y = 192.671829503468

y = 193

Footnotes

• note1: if the variable is in the trees, aka exponent, then log it down. In other words, we use logs to isolate the exponent.
• note2: use the log rule that Log(A^B) = B*Log(A) which is the actual act of pulling down the exponent and it helps us isolate it.