4)) Polonium- 217 is a radioactive substance that decays rapidly. If you start with 10 grams of polonium- 217 , the amount left after \( t \) seconds can be modeled by the expression \( 10\left(\frac{3}{5}\right)^{t} \) 4) What does the quantity \( \left(\frac{3}{5}\right)^{t} \) represent? The number of seconds it takes for only half of the sample to be left. The fraction of the original amount of polonium-217 that remains after \( t \) The polonium- 217 that remains after \( t \) seconds. seconds. \( \begin{array}{l}\text { The number of seconds it takes for } 10 \text { grams of polonium- } 217 \text { to decay to } t \\ \text { grams. }\end{array} \)

The fraction of the original amount of polonium-217 that remains after \( t \) seconds is represented by \( \left(\frac{3}{5}\right)^{t} \). This expression shows how the remaining quantity of the substance decreases over time, providing a clear indication of its decay rate as influenced by its radioactive properties. In practical terms, this model assists scientists in understanding the behavior of radioactive substances like polonium-217 in real-world applications, such as nuclear medicine or radioactive waste management. By knowing the remaining fraction at any time \( t \), researchers can make informed decisions regarding safety protocols or treatment plans based on the decay of isotopes.