Question

1. a certain bacteria doubles every hour. if there are 8 bacteria to begin with, how many will there be in 12 hours?

Explanation:

Step1: Identify the growth formula

The bacteria grow exponentially and double every hour. The formula for exponential growth when the quantity doubles every time period is \( N = N_0\times2^t \), where \( N_0 \) is the initial quantity, \( t \) is the time in hours. Here, \( N_0 = 8 \) and \( t = 12 \).

Step2: Substitute the values into the formula

Substitute \( N_0 = 8 \) and \( t = 12 \) into the formula \( N = 8\times2^{12} \).
First, calculate \( 2^{12}=4096 \).
Then, \( N = 8\times4096 = 32768 \).

Answer:

32768