The question (growth rate) deals with exponential functions. Growth occurs at a constant growth rate and is modeled by the standard equation:
[tex]\begin{gathered} y=ab^x \\ where\colon a=initial\text{ }amount \\ b=growth\text{ }factor \\ b=1+r \\ x=number\text{ }of\text{ }hours \end{gathered}[/tex]
We were given the following information from the question:
Initial or starting amount of bacteria cells, a = 800
Growth rate, r = 3.2% =3.2/100 = 0.032
Time, x = 35 hours
We will proceed to substitute these variables into the growth equation, we have:
[tex]\begin{gathered} y=ab^x \\ b=1+r=1+0.032=1.032 \\ \Rightarrow y=a(1+r)^x \\ y=a(1+r)^x \\ \text{Substituting the values of the variables into the equation, we have:} \\ y=800(1.032)^{35} \\ y=800(3.01155) \\ y=2409.24\approx2409 \\ y=2409 \end{gathered}[/tex]
Therefore, after 35 hours, the number of bacteria cells would have increased from 800 to 2409
We will proceed to graph the growth function as shown below:
