Question

directions: type the correct answer in the box. use numerals instead of words.
in a sterile environment, a single cell of bacteria is placed on a sandwich for an experiment. the amount of bacteria doubles each hour.
complete the following sentence that describes the relationship between the units of bacteria grown and the time required for its growth, t, in hours.
after hour(s), the bacteria count on the sandwich reaches 2,048 units.

Explanation:

Step1: Determine the formula

The formula for exponential growth is \(N = N_0\times2^t\), where \(N_0 = 1\) (initial amount of bacteria), \(N = 2048\) (final amount of bacteria), and \(t\) is the time in hours.

Step2: Substitute values into the formula

Substitute \(N_0 = 1\) and \(N = 2048\) into \(N = N_0\times2^t\), we get \(2048=1\times2^t\), so \(2^t = 2048\).

Step3: Find the value of \(t\)

Since \(2048 = 2^{11}\) (because \(2\times2\times\cdots\times2\) (11 times) \(= 2048\)), then \(t = 11\).

Answer:

11