91Ó°ÊÓ

After 7 days, a particular radioactive substance decays to half of its original amount. Find the decay rate of this substance.

Use a logarithmic transformation to find a linear relationship between the given quantities and graph the resulting linear relationship on a log-log plot. $$ y=5 x^{3} $$

After 5 days, a particular radioactive substance decays to \(37 \%\) of its original amount. Find the half-life of this substance.

Find the center and the radius of the circle given by the equation $$ x^{2}+y^{2}+2 x-4 y+1=0 $$

(a) Convert \(75^{\circ}\) to radian measure. (b) Convert \(\frac{17}{17} \pi\) to degree measure.

Use a logarithmic transformation to find a linear relationship between the given quantities and graph the resulting linear relationship on a log-log plot. $$ y=x^{-2} $$

Polonium \(210\left(\mathrm{Po}^{210}\right)\) has a half-life of 140 days. (a) If a sample of \(\mathrm{Po}^{210}\) has a mass of 300 micrograms, find \(\mathrm{a}\) formula for the mass after \(t\) days. (b) How long would it take this sample to decay to \(20 \%\) of its original amount?

Use a logarithmic transformation to find a linear relationship between the given quantities and graph the resulting linear relationship on a log-log plot. $$ y=6 x^{-1} $$

The half-life of \(C^{14}\) is 5730 years. Suppose that wood found at an archeological excavation site contains about \(35 \%\) as much \(\mathrm{C}^{14}\) (in relation to \(\mathrm{C}^{12}\) ) as does living plant material. Determine when the wood was cut.

(a) Convert \(-15^{\circ}\) to radian measure. (b) Convert \(\frac{3}{4} \pi\) to degree measure.