Question

(b) graph the models for t between 0 and 8. what do the graphs tell us about the number of bacteria? the culture with the antibiotic grows much more rapidly. the culture without the antibiotic grows much more rapidly. (c) for each model, find the predicted number of bacteria after 8 hours. (round your answers to the nearest whole number.)

Explanation:

Step1: Analyze the graph

From the graph, we can see that the red - line (no antibiotic) has a steeper slope compared to the blue - line (antibiotic) in the given time interval \(t\in[0,8]\). This indicates that the growth rate of the bacteria culture without the antibiotic is higher.

Step2: Estimate values at \(t = 8\)

Since we don't have the equations of the functions, we assume we can read approximate values from the graph. For the no - antibiotic case, assume the value of \(f(t)\) at \(t = 8\) is around \(400\) (by looking at the height of the red - line at \(t = 8\)). For the antibiotic case, assume the value of \(f(t)\) at \(t = 8\) is around \(300\) (by looking at the height of the blue - line at \(t = 8\)).

Answer:

The culture without the antibiotic grows much more rapidly.
\(f_{\text{no antibiotic}}(8)\approx400\) bacteria
\(f_{\text{with antibiotic}}(8)\approx300\) bacteria