Question

part 3 of 4
hw score: 39.12%, 9.39 of 24 points
points: 0 of 1
owing for the function given below.
number of bacteria), where time is measured in hours of a day
be an appropriate domain and range for the function.
a rough sketch of a graph of the function.
discuss the validity of the graph as a model of the true function.
rough sketch of a graph of the function. choose the correct graph below. let t represent time in hours and b represent
f bacteria.
ob.
oc.
od.
clear all
check answe

Explanation:

To determine the correct graph for the bacteria growth function, we analyze the axes and the nature of bacterial growth:

Key Observations:

• Axes Interpretation: The function models the number of bacteria (\( b \)) over time (\( t \) in hours). Thus, the vertical axis should represent \( b \) (bacteria), and the horizontal axis should represent \( t \) (time in hours).
• Growth Pattern: Bacterial growth is typically exponential (or logistic), meaning the number of bacteria (\( b \)) increases with time (\( t \)). The graph should show \( b \) (vertical) increasing as \( t \) (horizontal) increases.

Analyzing the Options:

• Option B: Vertical axis is \( t \) (time) and horizontal axis is unclear—incorrect, as time should be the independent variable (horizontal axis).
• Option C: Vertical axis is \( b \) (bacteria), horizontal axis is \( t \) (time). The graph shows \( b \) increasing with \( t \), consistent with bacterial growth (e.g., logistic growth, leveling off as resources limit growth).
• Option D: The graph starts with very low \( b \) and spikes late, which is less typical for standard bacterial growth models (usually gradual, then rapid, or logistic).

Since bacterial growth (e.g., logistic or exponential) is represented by \( b \) (vertical) increasing with \( t \) (horizontal), and Option C aligns with this (vertical axis = bacteria, horizontal = time, growth pattern consistent), it is the correct choice.

Answer:

C. (Graph with vertical axis \( b \) (bacteria) and horizontal axis \( t \) (hours), showing increasing \( b \) over \( t \))