Question

Clue #1: It’s getting’ hot in here! This suspect who committed this dastardly deed not only robbed the lyrics from Nelly’s 2013 hit Hot in Here, but he or she is developing a new strain of antibiotic-resistant bacteria that could wipe out hip hop artists around the world (although some might see this fortuitous...). Bacterial growth is slowed if the bacteria are grown in colder temperatures. Two functions are used to model the population of bacteria (where t = the number of minutes since infection and () is the number of bacteria colonies at room temperature and () is the number of bacterial colonies when refrigerated). Assuming there are plenty of nutrients for the bacteria, what will be the difference in the number of colonies projected after 5 hours of unrestricted growth?

Answer 1

The given functions are

`\begin{gathered} f(t)=20.52e^(0.0195t)\rightarrow(1) \\ g(t)=11.35e^(0.0111t)\rightarrow(2) \end{gathered}`

Where t is the time in minutes

f(t) and g(t) are the numbers of bacterias

We need to find the difference in 5 hours

Change the time to minutes by multiplying 5 hours by 60, then substitute it in the functions to find the values, then subtract them

`\begin{gathered} t=5*60 \\ t=300 \end{gathered}`
`\begin{gathered} f(300)=20.52e^(0.0195(300)) \\ f(300)=7125.25(2d\mathrm{}p) \end{gathered}`
`\begin{gathered} g(300)=11.35e^(0.0111t) \\ g(300)=317.10(2d\mathrm{}p) \end{gathered}`

Now, we will subtract them to find the difference

`\begin{gathered} D=7125.25-317.10 \\ D=6808.15 \end{gathered}`

Then the difference is about 6808