Question

Ok how would I use this function to calculate for the graph?

Answer 1

Given:

The given function is

$g(x)=21log_2(x+1)+85$

Required:

We have to find the values of g(x) for the values of x given in the table and then plot the graph.

Explanation:

At x=0,

$\begin{gathered} g(x)=21\text{ }log_2(0+1)+85 \\ =21\text{ }log_2(1)+85 \end{gathered}$$\begin{gathered} =21\times0+1 \\ =1 \end{gathered}$

At x=25,

$\begin{gathered} g(x)=21\text{ }log_2(25+1)+85 \\ =21\text{ }log_2(26)+85 \end{gathered}$$\begin{gathered} =21(log_2(2\times13)+85 \\ =21+77.709+85 \end{gathered}$$=183.709$

At x=50,

$\begin{gathered} g(x)=21\text{ }log_2(50+1)+85 \\ =21\text{ }log_2(51)+85 \end{gathered}$$\begin{gathered} =119.12+85 \\ =204.12 \end{gathered}$

At x=75,

$\begin{gathered} g(x)=21\text{ }log_2(75+1)+85 \\ =21\text{ }log_2(76)+85 \end{gathered}$$\begin{gathered} =131.21+85 \\ =216.21 \end{gathered}$

At x=100,

$\begin{gathered} g(x)=21\text{ }log_2(100+1)+85 \\ =21\text{ }log_2(101)+85 \end{gathered}$$\begin{gathered} =139.82+85 \\ =224.82 \end{gathered}$

Hence the table becomes

We now draw the graph with these points

Final answer:

Hence the final answer is the table above and the graph drawn above.