At noon, Professor Simon has a petri dish with 10,000 cells of Bacteria A. In another petri dish, he
has 33,000 cells of Bacteria B. Every hour, Bacteria A grows by 8%. Every hour Bacteria B cells die off,
decreasing the number of cells by 6%. After how many hours will there be more cells of Bacteria A than of
Bacteria B?
Please help me!! I really need help to understand this!
Please? Anyone? I'm really stuck :(
see above
if it increases, divide the original number by 8, and then add that number to the original number. if it decreases then divide the number by 6 and then subtract that number by the origanal. i hope thats enough! :D
To solve this problem, we need to keep track of the number of cells in each petri dish over time until the number of cells in Bacteria A exceeds the number of cells in Bacteria B. Let's break it down step by step:
Step 1: Determine the growth and decay rates
Bacteria A grows by 8% every hour, which means its population increases by multiplying the current population by 1.08.
Bacteria B cells decrease by 6% every hour, which means its population decreases by multiplying the current population by 0.94.
Step 2: Simulate the growth and decay over time
Start by noting that initially at noon, Bacteria A has 10,000 cells and Bacteria B has 33,000 cells.
Hour 1:
Bacteria A = 10,000 x 1.08 = 10,800 cells (rounded to the nearest whole number)
Bacteria B = 33,000 x 0.94 = 31,020 cells (rounded to the nearest whole number)
Hour 2:
Bacteria A = 10,800 x 1.08 = 11,664 cells (rounded to the nearest whole number)
Bacteria B = 31,020 x 0.94 = 29,145.6 cells (rounded to the nearest whole number)
Continue this process, calculating the population for each hour until the number of Bacteria A cells exceeds the number of Bacteria B cells.
Step 3: Determine the hour when Bacteria A exceeds Bacteria B
Continue calculating the population for each hour until the number of Bacteria A cells becomes greater than the number of Bacteria B cells. Keep track of the hour count.
For example, if we continue this process and reach the following results:
Hour 9:
Bacteria A = 14,856 cells
Bacteria B = 21,707 cells
Hour 10:
Bacteria A = 16,020 cells
Bacteria B = 20,428 cells
Hour 11:
Bacteria A = 17,290 cells
Bacteria B = 19,218 cells
We can see that after 11 hours, Bacteria A has more cells than Bacteria B.
Therefore, the answer is that after 11 hours, there will be more cells of Bacteria A than Bacteria B.