Santr 109 (a fictitious substance) decays by about 6% every day. How much of a 84 pound sample remains after:
(a) 7 days
(b) 3 weeks
(b) 48 days
To calculate how much of the sample remains after a certain number of days, you will need to subtract the percentage of decay from the original sample size for each given time period.
(a) After 7 days:
To calculate the remaining amount after 7 days, subtract 6% of the original size (84 pounds) for 7 days.
Remaining amount = 84 pounds - (0.06 * 84 pounds * 7 days)
Remaining amount = 84 pounds - (0.06 * 84 pounds * 7)
Remaining amount = 84 pounds - (5.04 pounds)
Remaining amount ≈ 78.96 pounds
Therefore, approximately 78.96 pounds of the sample remains after 7 days.
(b) After 3 weeks:
Note that there are 7 days in a week, so 3 weeks equal 3 * 7 = 21 days. Using this information, you can calculate the remaining amount.
Remaining amount = 84 pounds - (0.06 * 84 pounds * 21 days)
Remaining amount = 84 pounds - (0.06 * 1764 pounds)
Remaining amount ≈ 84 pounds - 105.84 pounds
Remaining amount ≈ 78.16 pounds
Therefore, approximately 78.16 pounds of the sample remains after 3 weeks.
(c) After 48 days:
Remaining amount = 84 pounds - (0.06 * 84 pounds * 48 days)
Remaining amount = 84 pounds - (0.06 * 4032 pounds)
Remaining amount ≈ 84 pounds - 241.92 pounds
Remaining amount ≈ -157.92 pounds
In this case, the calculation results in a negative value, indicating that the decay has exceeded the original amount. Therefore, there is no remaining sample after 48 days.
Please note that in this explanation, we assumed a linear decay rate of 6% per day for the given substance.