Question

Please help me with this math problem so I can assist my son on how this should be done.

Answer 1

The question (growth rate) deals with exponential functions. Growth occurs at a constant growth rate and is modeled by the standard equation:

`\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}`

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:

`\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}`

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: