Answer :
Solution
- The question gives us the following equation
[tex]\begin{gathered} h=2.25w+20 \\ where, \\ h=height\text{ of a small sunflower} \\ w=\text{ Number of weeks after it was planted} \end{gathered}[/tex]- We are required to determine what 20 represents.
- In order to determine what 20 represents, let us first try to find the height of the sunflower for some weeks.
- That is,
[tex]\begin{gathered} \text{ Week 1:} \\ w=1, \\ h=2.25(1)+20 \\ h=2.25+20 \\ \\ \text{ Week 2:} \\ w=2, \\ h=2.25(2)+20 \\ h=4.5+20 \\ \\ \text{ Week 3:} \\ w=3, \\ h=2.25(3)+20 \\ h=6.75+20 \\ \\ And\text{ so on...} \end{gathered}[/tex]- From the above illustration, we can see that no matter the week we consider, or the height the sunflower reaches, we must always add 20.
- This means that 20 is independent of the number of weeks since the sunflower has been planted and also independent of the height of the sunflower after its planting.
- However, we have not tried one number. That is for week 0. This pertains to the week before the sunflower was planted.
[tex]\begin{gathered} h=2.25w+20 \\ w=0 \\ h=2.25(0)+20 \\ h=20 \end{gathered}[/tex]- Here, we get that the height (h) is actually equal to the value 20 when the week is set to 0.
- This implies that the sunflower was at a height of 20 before it was planted in week 1.
- Thus, we can conclude that 20 corresponds to the height of the sunflower when it was planted
Final Answer
20 corresponds to the height of the sunflower when it was planted