Respuesta :
Given the information, we know that the groth is linear, and also we have two points: (2,4) and (5,5.5). Then we can find the equation in the following way:
[tex]\begin{gathered} (x_1,y_1)=(2,4) \\ (x_2,y_2)=(5,5.5) \\ \text{slope:}_{} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{5.5-4}{5-2}=\frac{1.5}{3}=0.5 \\ m=0.5 \\ \text{ point-slope formula:} \\ y-y_1=m(x-x_1) \\ \Rightarrow y-4=0.5(x-2) \\ \Rightarrow y-4=0.5x-1 \\ \Rightarrow y=0.5x-1+4=0.5x+3 \\ y=0.5x+3 \end{gathered}[/tex]If h are the inches and n the weeks, then the equation is:
[tex]h=0.5n+3[/tex]Now, if we want to know how tall will be the plant in 10 weeks, we just make n=10 and find the value of h:
[tex]\begin{gathered} n=10 \\ h=0.5n+3 \\ \Rightarrow h=0.5\cdot10+3=5+3=8 \\ h=8 \end{gathered}[/tex]therefore, after 10 weeks, the plant will be 8 inches.
Finally, to find out how many weeks will it take the plant to grow 20 inches, we make h=20 and solve for n:
[tex]\begin{gathered} h=20 \\ h=0.5n+3 \\ \Rightarrow20=0.5n+3 \\ \Rightarrow20-3=0.5n \\ \Rightarrow n=\frac{17}{0.5}=34 \\ n=34 \end{gathered}[/tex]therefore, the plant will be 20 inches tall in 34 weeks
