11. Find the exponential function y = Cekx that passes through the two given points. Round your values of C and k to four decimal places.
a. y = 5e-0.4159x
b. y = 5e-0.5756x
c. y = 5e0.2266x
d. y = 5e0.2763x
e. y = 5e-3.6889x
12. The isotope 14C has a half-life of 5,715 years. Given an initial amount of 11 grams of the isotope, how many grams will remain after 500 years? After 5,000 years? Round your answers to four decimal places.
a. 7.2469 gm, 4.1988 gm
b. 6.2117 gm, 3.5989 gm
c. 10.3528 gm, 5.9982 gm
d. 4.1411 gm, 2.3993 gm
e. 12.4233 gm, 7.1979 gm
13. The half-life of the radium isotope Ra-226 is approximately 1,599 years. If the initial quantity of the isotope is 38 g, what is the amount left after 1,000 years? Round your answer to two decimal places.
a. 24.63 g
b. 30.60 g
c. 25.13 g
d. 11.88 g
e. 12.32 g
14. The isotope 14C has a half-life of 5,715 years. After 2,000 years, a sample of the isotope is reduced to 1.2 grams. What was the initial size of the sample (in grams)? How much will remain after 20,000 years (i.e., after another 18000 years)? Round your answers to four decimal places.
a. 1.0706, 0.0947
b. 2.4471, 0.2164
c. 1.5294, 0.1352
d. 2.1412, 0.1893
e. 1.9883, 0.1758
15. The isotope 239Pu has a half-life of 24,100 years. After 10,000 years, a sample of the isotope is reduced 1.6 grams. What was the initial size of the sample (in grams)? How large was the sample after the first 1,000 years? Round your answers to four decimal places.
a. 2.1332, 2.0727
b. 2.7731, 2.6945
c. 1.2799, 1.2436
d. 1.7065, 1.6582
e. 1.0666, 1.0364
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