Question

14 mark for review
bacteria are growing in a liquid growth medium. there were 300,000 cells per milliliter during an initial observation. the number of cells per milliliter doubles every 3 hours. how many cells per milliliter will there be 15 hours after the initial observation?
a 1,500,000
b 2,400,000
c 4,500,000
d 9,600,000

Explanation:

Step1: Find the number of doubling periods

The time elapsed is 15 hours, and the doubling period is 3 hours. So the number of doubling periods \( n=\frac{15}{3} = 5\).

Step2: Apply the exponential growth formula

The formula for exponential growth (doubling) is \( N = N_0\times2^n\), where \( N_0 = 300000\) (initial number of cells), and \( n = 5\).
Substitute the values: \( N=300000\times2^5\).
Calculate \( 2^5=32\), then \( N = 300000\times32=9600000\).

Answer:

D. 9,600,000