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

D) write an explanation model that represents the total infected for any given dayE-example-1

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

Step-by-step 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

User Nuno Cruces
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