Cellular Growth Leticia Cox is a biochemist. She is testing two different types of drugs that induce cell growth. She has selected two cultures of 1000 cells each. To culture A, she administers a drug that raises the number of cells by 200 each day and every day thereafter. Culture B gets a drug that increases cell growth by 8% each day and everyday thereafter. a. Assuming no cells die, how many cells will have grown in each culture by the end of the seventh day? b. At the end of one month's time, which drug will prove to be more effective in promoting cell growth? Explain

Question

Mathematics

Zander

12 November, 15:57

Cellular Growth Leticia Cox is a biochemist. She is testing two different types of drugs that induce cell growth. She has selected two cultures of 1000 cells each. To culture A, she administers a drug that raises the number of cells by 200 each day and every day thereafter. Culture B gets a drug that increases cell growth by 8% each day and everyday thereafter. a. Assuming no cells die, how many cells will have grown in each culture by the end of the seventh day? b. At the end of one month's time, which drug will prove to be more effective in promoting cell growth? Explain

+3

Answers (1)

Know the Answer?

Quincy · Answer 1

Culture A will grow by 200 cells a day. Therefore we can determine the number of cells of culture A after 7 days with simple addition: 1000 + 200 + 200 + 200 + 200 + 200 + 200 + 200 = 2400.

Culture B will grow by 8 percent a day. So from the initial 1000 cells, we employ the following equation.

1000 + 80 = 1080; 1080 + 86,4 = 1166,4; 1166,4 + 93,3 = 1259,7; 1259,7 + 100,78 = 1461,26; 1461,26 + 116,9 = 1518,16; 1518,16 + 121,45 = 1639,6; 1639,6 + 131,17 = 1770,77.

For the purposes of cell culture, one cannot have half a cell, so we round to the nearest whole number after calculation, and we have 1770 cells after one week of growth.

Assuming one month is four weeks long, we can determine that culture A will have 2400 x 4 cells after four weeks of growth, which equals to 9600 cells.

To calculate the growth of culture B after four weeks, we can use the first weeks rate of growth and employ that to the following weeks.

So, the first weeks growth was 1000/1770 x 100 = 56 %.

Now for the second week, we add 56 % of 1770 to 1770, which equals to 991 + 1770 = 2761.

For the third week, we do the same, 56 % of 2761, which equals 1546 + 2761 = 4307.

For the final week, the same applies, 56% of 4307, which equals 2412 + 4307 = 6719.

Assuming that none of the cells died, the drug that was applied to culture A was more effective as more cells were grown in a month's time compared to that in culture B.