0%
0 / 1 answered
Logarithmic Function Context and Data Modeling Practice Test
•1 QuestionsQuestion
1 / 1
Q1
A chemistry class measures a radioactive sample that steadily loses mass. The instructor emphasizes that the process is exponential with a constant decay rate, so a log transformation linearizes the data. They model mass by $m(t)=m_0(1-d)^t$ and rewrite it as $\log_{10}(m)=\log_{10}(m_0)+t,\log_{10}(1-d)$. Here the logarithm uses base 10, and the slope equals $\log_{10}(1-d)$. The table gives measured masses in grams at integer hours. Students are asked to pick the log-linear equation that matches the measurements.
Based on the scenario, which logarithmic equation represents the scenario described?
A chemistry class measures a radioactive sample that steadily loses mass. The instructor emphasizes that the process is exponential with a constant decay rate, so a log transformation linearizes the data. They model mass by $m(t)=m_0(1-d)^t$ and rewrite it as $\log_{10}(m)=\log_{10}(m_0)+t,\log_{10}(1-d)$. Here the logarithm uses base 10, and the slope equals $\log_{10}(1-d)$. The table gives measured masses in grams at integer hours. Students are asked to pick the log-linear equation that matches the measurements.
Based on the scenario, which logarithmic equation represents the scenario described?