A medical device uses the radioactive isotope cesium 137. The function f(t) = 28(0.5) 30 gives the number of
grams of the isotope that remain t hours after its introduction to the device. Which statement is true?
O Every 30 hours, the number of grams of the isotope doubles.
O After t hours, there are half as many grams of the isotope as at the start.
The device started with 28 grams of the isotope.
The correct statement is: After t hours, there are half as many grams of the isotope as at the start.
This can be seen by looking at the function f(t) = 28(0.5)^t. The function is an exponential decay function, with a base of 0.5. This means that for each hour that passes, the number of grams of the isotope is halved. This matches the statement that after t hours, there are half as many grams of the isotope as at the start.
The statement "Every 30 hours, the number of grams of the isotope doubles" is not true. In fact, every 30 hours, the number of grams of the isotope is halved, because the exponent in the function is t/30.