Question

the tables show functions representing the growth of two types of bacteria on certain days within an experiment that lasted a total of 10 days. bacteria a time (days) 0 2 4 6 bacteria count 60 240 960 3,840 bacteria b time (days) 0 1 3 5 bacteria count 90 180 720 2,880 how do the functions in the table compare? since x - intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria b than bacteria a at the start. since y - intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria b than bacteria a at the start. since the maximum value in the table for bacteria a is greater than the maximum value in the table for bacteria b, bacteria a has a faster growth rate than bacteria b. since the minimum value in the table for bacteria a is less than the minimum value in the table for bacteria b, bacteria a has a slower growth rate than bacteria b.

Explanation:

Step1: Identify the starting - point value

The starting - point of the experiment is when time \(x = 0\). The value of the function at \(x = 0\) is the \(y\) - intercept. For bacteria A, when \(x=0\), the bacteria count \(y = 60\). For bacteria B, when \(x = 0\), the bacteria count \(y=90\).

Step2: Analyze the growth - rate concept

The growth rate is not determined by the minimum or maximum values in the table alone. The growth rate is related to how the function changes over time. The \(y\) - intercept represents the initial amount of bacteria.

Answer:

Since y - intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.