Questions: A tumor is injected with 0.6 grams of Iodine-125, which has a decay rate of 1.15% per day. Write an exponential model representing the number of grams f of Iodine-125 remaining in the tumor after t days. f(t)=

Solution Steps

To model the decay of Iodine-125, we use the exponential decay formula. The general form of the exponential decay model is \( f(t) = a \times (1 - r)^t \), where \( a \) is the initial amount, \( r \) is the decay rate, and \( t \) is the time in days. Here, \( a = 0.6 \) grams and \( r = 0.0115 \) (since 1.15% is 0.0115 in decimal form).

The amount of Iodine-125 remaining in the tumor after \( t \) days can be modeled using the exponential decay formula: \[ f(t) = a \times (1 - r)^t \] where \( a = 0.6 \) grams (the initial amount) and \( r = 0.0115 \) (the decay rate).

To find the amount of Iodine-125 remaining after \( t = 10 \) days, we substitute \( t \) into the model: \[ f(10) = 0.6 \times (1 - 0.0115)^{10} \] Calculating this gives: \[ f(10) \approx 0.5345 \text{ grams} \]

Final Answer