Respuesta :
Step 1: Write out the general equation for a linear function
[tex]\begin{gathered} \text{The general equation for a linear function is} \\ y=mx+c \\ \text{Where} \\ y=\text{dependent variable} \\ x=\text{independent variable} \\ m=\text{slope} \\ c=\text{intercept on the y-axis} \end{gathered}[/tex]Step 2: Write out a linear function for the height and the amount of time
If h represents height and t represents time. The equation of the linear function connecting h and t would be
[tex]h=mt+c[/tex]Step 3: Write out the general formula for finding the equation of linear function given two different coordinates
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]For the function of h and t, the formula would be
[tex]\begin{gathered} \frac{h-h_1}{t-t_1}=\frac{h_2-h_1}{t_2-t_1} \\ \text{where} \\ h_1=\text{initiah height=24cm} \\ h_2=\text{final height=18.4cm} \\ t_1=\text{initial time=5hours} \\ t_2=\text{final time=19hours} \end{gathered}[/tex]Substitute for the given parameters in the formula
[tex]\frac{h-24}{t-5}=\frac{18.4-24}{19-5}[/tex][tex]\begin{gathered} \frac{h-24}{t-5}=\frac{-5.6}{14} \\ \frac{h-24}{t-5}=\frac{-2}{5} \\ \text{cross multiply} \\ 5(h-24)=-2(t-5) \\ 5h-120=-2t+10 \\ 5h=-2t+10+120 \\ 5h=-2t+130 \end{gathered}[/tex]Divide through by 5
[tex]\begin{gathered} \frac{5h}{5}=\frac{-2t}{5}+\frac{130}{5} \\ h=\frac{-2t}{5}+26 \end{gathered}[/tex]The above function connect the height and the amount of time together
Step 4: Find the height of the candle after 10 hours
[tex]\begin{gathered} \text{When t=10} \\ h=\frac{-2(10)}{5}+26 \\ h=-4+26 \\ h=22\operatorname{cm} \end{gathered}[/tex]Hence, the height of the candle after 10 hours is 22cm
