Precalculus question 1

Question

At the beginning of an experiment, a scientist has 316 grams of radioactive goo. After 195 minutes, her sample has decayed to 4.9375 grams. 

What is the half-life of the goo in minutes?     

Find a formula for G(t), the amount of goo remaining at time t. G(t)=    

How many grams of goo will remain after 17 minutes? 

Answer 1

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Answer 2

4.9375= 316e^195r

4.9375/316 = e^195r

r = ln(4.9375/316)/195=about -.02133 = about a 2% decay rate per minute

G(t) = 316e^-.02133t= Goo at time t

1/2 = -e^.02133t t=half life

ln(.5)= -.02133t

t = -ln(.5)/.02133= about 32 1/2 minutes half life

in 17 minutes, G(17) = 316e^-.02133(17)

= about 219.89