Question

the table below shows the amount of grams of iodine-125 left after several days. what is the decay factor for this data? round to two decimal places, if necessary.

days | grams of iodine-125 remaining
5 | 247.32
6 | 244.86
7 | 242.42
8 | 240.01
9 | 237.62

Explanation:

Step1: Recall decay factor formula

For exponential decay, the formula is \( A = A_0 \cdot r^t \), where \( r \) is the decay factor. To find \( r \), we can take the ratio of the amount at day \( t + 1 \) to the amount at day \( t \). Let's take the first two consecutive days, say day 5 and day 6.

Step2: Calculate the ratio

The amount at day 5 is \( 247.32 \) grams, and at day 6 is \( 244.86 \) grams. The decay factor \( r \) is \( \frac{244.86}{247.32} \).
Calculating this: \( \frac{244.86}{247.32} \approx 0.99 \) (we can check with other consecutive days, like day 6 and day 7: \( \frac{242.42}{244.86} \approx 0.99 \), day 7 and day 8: \( \frac{240.01}{242.42} \approx 0.99 \), day 8 and day 9: \( \frac{237.62}{240.01} \approx 0.99 \), so the decay factor is consistent around 0.99).

Answer:

\( 0.99 \)