Question

D) write an explanation model that represents the total infected for any given dayE) grab the data and state the domain and the range

Answer 1

$\begin{gathered} f(x)=4\cdot2^x \\ \text{where x is the number of days} \end{gathered}$

Explanation

Step 1

make the table

$\begin{gathered} \text{days total infected} \\ 0\text{ }\rightarrow\text{4} \\ 1\text{ }\rightarrow\text{4+4=8} \\ 2\text{ }\rightarrow\text{4+4+4+4=16} \end{gathered}$

as we can see for every day the number of total infected is twice the previos, we can model this by the function

$\begin{gathered} 0\rightarrow4\cdot2^0=4\cdot1=4 \\ 1\rightarrow4\cdot2^1=4\cdot2=8 \\ 2\rightarrow4\cdot2^2=4\cdot4=16 \\ 3\rightarrow4\cdot2^3=4\cdot8=32 \\ \ldots \\ \text{..} \\ x\rightarrow4\cdot2^x \end{gathered}$

so, we have a pattern, that is the function

$f(x)=4\cdot2^x$

where f(x) is the total infected and x in the number of days

Step 2

the domain of a function is the set of vales x can take, in this case, we are taking x as days, so it must be greater than 0, so de domain is

$\begin{gathered} \text{from zero to infinite} \\ (0,\infty)\text{ or x}>0 \end{gathered}$

the range is all values y can takes, in this case y represents the total of infected, so it must be greater or equal than 4 ( 4 people were initially infected )

$\begin{gathered} \text{range} \\ \lbrack4,\infty\text{) or x}\ge4 \end{gathered}$

I hope this helps you