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There are 1,200 bacteria in a lab dish. The number of bacteria decreases 10% per day. Compare the decrease in the number of bacteria for days 1 to 3 with the decrease for days 4 to 6. Use the drop-down menu to complete the sentence.

The number of bacteria decreases:

A) less from day 1 to day 3 than from day 4 to day 6.
B) more from day 1 to day 3 than from day 4 to day 6.
C) the same from day 1 to day 3 as from day 4 to day 6.
D) exponentially from day 1 to day 3.

User Lbergnehr
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1 Answer

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Final answer:

The number of bacteria decreases by a larger amount from day 1 to day 3 than from day 4 to day 6 because the initial number is higher in the first three days, and a constant percentage decrease results in a larger absolute number reduction when the number is larger.

Step-by-step explanation:

When analyzing the decrease in the number of bacteria in a lab dish that initially contains 1,200 bacteria and decreases by 10% each day, we need to calculate the absolute numbers for each period to compare them. On the first day, a 10% decrease will result in 120 bacteria being lost. On day two, the number is again decreased by 10%, but this time from 1,080 (1,200 - 120) bacteria, losing 108 bacteria, leaving 972 bacteria in the dish. On the third day, with 972 bacteria remaining, a loss of 10% equals 97.2 bacteria, for a new total of approximately 874.8 bacteria.

For days four to six, we start with the number of bacteria from the end of day three and apply the same 10% decrease each day. Each subsequent day, the number of lost bacteria is 10% of a smaller number than the day before, causing the absolute decrease in bacteria to be smaller each day. This pattern will continue, yielding a smaller decrease from days four to six compared to days one to three.

Therefore, the correct choice from the dropdown menu is: B) more from day 1 to day 3 than from day 4 to day 6, because a constant percentage decrease from a smaller initial number results in a smaller absolute decrease in number of bacteria.

User Kischa
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