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
5 289.55
6 283.81
7 278.19
8 272.69
9 267.29

show your work here

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Explanation:

Step1: Recall Decay Factor Formula

The decay factor \( b \) in an exponential decay model \( y = a \cdot b^x \) is found by dividing a subsequent amount by the previous amount (since each day, the amount is multiplied by \( b \)). So, \( b=\frac{\text{Amount at day } n + 1}{\text{Amount at day } n} \).

Step2: Calculate Decay Factor (First Pair)

Take the amount at day 6 (\( 283.81 \)) and divide by the amount at day 5 (\( 289.55 \)):
\( b=\frac{283.81}{289.55}\approx0.98 \).

Step3: Verify with Another Pair (Optional)

Check with day 7 and day 6: \( \frac{278.19}{283.81}\approx0.98 \).
Or day 8 and day 7: \( \frac{272.69}{278.19}\approx0.98 \).
Or day 9 and day 8: \( \frac{267.29}{272.69}\approx0.98 \). All confirm the decay factor.

Answer:

\( 0.98 \)