Question

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 every day thereafter. Assuming no cells die, how many cells will have grown in each culture by the end of the seventh day? a. Culture A: 1400 cells Culture B: 713 cells c. Culture A: 713 cells Culture B: 1400 cells b. Culture A: 800 cells Culture B: 517 cells d. Culture A: 517 cells Culture B: 800 cells

Answer 1

1. Culture A.

Since the number of cells increases by 200 each day and every day thereafter, then after seven days the number of cells will increase by

$200\cdot 7=1,400.$

2. Culture B.

The initial number of cells was 1,000. Since the number of cells increases 8% each day and every day thereafter, then after seven days the number of cells will be

$1,000\cdot (1.08)^7\approx 1,713.$

The number of cells that have grown by the end of the seventh day is

1,713-1,000=713.

Answer: option A -- Culture A: 1400 cells Culture B: 713 cells