14 mark for review bacteria are growing in a liquid growth medium. there were 300,000 cells per milliliter…

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

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

Answer

Answer:

D. 9,600,000

Explanation:

Step1: Calculate the number of 3 - hour intervals

$15\div3 = 5$

Step2: Set up the exponential - growth formula

The initial number of cells $a = 300000$, and the growth factor is 2 for each 3 - hour interval. The formula for the number of cells $N$ after $n$ intervals is $N=a\times2^{n}$.

Step3: Substitute values into the formula

$N = 300000\times2^{5}$

Step4: Calculate $2^{5}$

$2^{5}=2\times2\times2\times2\times2 = 32$

Step5: Calculate the final number of cells

$N=300000\times32 = 9600000$