Unit 4, Lesson 7
Interpreting and Using Exponential Functions
Integrated Math 3
Practice
Problem 1
The half-life of carbon-14 is about 5,730 years. A fossil had 6 picograms of carbon-14 at one point in time. (A picogram is a trillionth of a gram, or \(1 \times 10^{\text-12}\) gram.) Which expression describes the amount of carbon-14, in picograms, \(t\) years after it was measured to be 6 picograms.
\(6 \boldcdot \left(\frac12\right)^{\frac{t}{5,730}}\)
\(6 \boldcdot \left(\frac12\right)^{5,730t}\)
\(6 \boldcdot (5,\!730)^{\frac12 t}\)
\(\frac12 \boldcdot (6)^{\frac{t}{5,730}}\)
Problem 2
The half-life of carbon-14 is about 5,730 years. A tree fossil was estimated to have about 4.2 picograms of carbon-14 when it died. (A picogram is a trillionth of a gram.) The fossil now has about 0.5 picogram of carbon-14. About how many years ago did the tree die? Show your reasoning.