The quantity Q of radioactive carbon remaining in a 300 - gram wood sample at time t is given by the expression

Q(t) = 300 e^{- 0.000324*t}.
How much radioactive carbon remains in the sample after
(a) 200 years, (b) 50000 years, (c) 125500 years?

what's the trouble? Just plug in the values for t.

For example,

Q(800) = 300 e^(-0.000324*800) = 231.5006

i just did it

Q(200) = 300 e^(-0.000324*200) = 281.176
But for b) and c) web work doesn't accept my answers
Q(50000) = 300 e^(-0.000324*50000) = 0.000028

maybe i should multiply by something...

To find the quantity of radioactive carbon remaining in the sample after a certain amount of time, we can substitute the given time value into the equation Q(t) = 300e^(-0.000324t).

(a) After 200 years:
To find the quantity of radioactive carbon remaining in the sample after 200 years, substitute t = 200 into the equation:
Q(200) = 300e^(-0.000324*200)
= 300e^(-0.0648)
≈ 220.191 grams

Therefore, approximately 220.191 grams of radioactive carbon will remain in the sample after 200 years.

(b) After 50,000 years:
To find the quantity of radioactive carbon remaining in the sample after 50,000 years, substitute t = 50,000 into the equation:
Q(50,000) = 300e^(-0.000324*50,000)
= 300e^(-16.2)
≈ 4.180 grams

Therefore, approximately 4.180 grams of radioactive carbon will remain in the sample after 50,000 years.

(c) After 125,500 years:
To find the quantity of radioactive carbon remaining in the sample after 125,500 years, substitute t = 125,500 into the equation:
Q(125,500) = 300e^(-0.000324*125,500)
= 300e^(-40.59)
≈ 0.017 grams

Therefore, approximately 0.017 grams of radioactive carbon will remain in the sample after 125,500 years.