Ten questions. The result tells you which lessons you may skip.
A ball dropped from \(1.25\,\text{m}\) keeps \(64\,\%\) of its height at every bounce. How high does it rise after the second bounce?
What is the slope of the curve \(y = e^x\) at \(x = 1\)?
A quantity decays as \(y_0e^{-t/\tau}\). What fraction is left after one time constant?
A capacitor discharges with \(\tau = 2\,\text{s}\). Its half-life is about
On the graph of \(y_0e^{-t/\tau}\), where does the tangent at \(t = 0\) meet the time axis?
A capacitor charges through a resistor with \(\tau = 1\,\text{s}\). What fraction of its final charge does it hold after \(3\,\text{s}\)?
Which of these equals \(\ln 6\)?
A sample falls to one tenth of its activity. How many time constants has that taken? Take \(\ln 10 = 2.3\).
Two identical loudspeakers each give \(80\,\text{dB}\) at a point. Together they give
To read a decay constant from measured counts \(A\) at times \(t\), which graph should be a straight line?