The quantity Q of radioactive carbon remaining in a 200-gram wood sample at time t is given by the expression
Q(t)=200e^(−0.000225⋅t).
How much radioactive carbon remains in the sample after 100500 years?
I just plugged in 100500 as t and got 3.02375 grams as an answer. Is this correct?
the 3.02375 is correct, but you lost a factor of 10^-8
So, what you really have is .03 micrograms
thanks
To find the amount of radioactive carbon remaining in the sample after 100500 years, we can substitute the value of t into the given expression for Q(t) and evaluate it. Let's go through the steps to calculate it correctly:
1. Start with the expression for Q(t):
Q(t) = 200e^(-0.000225t)
2. Substitute t = 100500 into the expression:
Q(100500) = 200e^(-0.000225(100500))
3. Simplify the exponent:
Q(100500) = 200e^(-22.6125)
4. Calculate the value of e^(-22.6125):
You can use a scientific calculator or an online calculator to evaluate this exponential value. In this case, e^(-22.6125) is approximately 2.859818 × 10^(-10).
5. Substitute the value of e^(-22.6125) back into the expression:
Q(100500) = 200 × 2.859818 × 10^(-10)
6. Multiply the value by 200:
Q(100500) ≈ 5.719636 × 10^(-8)
So, the correct answer is approximately 5.719636 × 10^(-8) grams of radioactive carbon remaining in the sample after 100500 years. It seems like the value you calculated, 3.02375 grams, is incorrect. Make sure to double-check the calculation process.