Question

At the beginning of spring, Nachelle planted a small sunflower in her backyard. The sunflower's height in inches, hh, after ww weeks, is given by the equation h=2.25w+20h=2.25w+20. What could the number 20 represent in the equation?The sunflower's final heightThe change in the sunflower's height for every one additional week.The sunflower's height when it was planted.The sunflower's height after one week.

Answer 1

Solution

- The question gives us the following equation

$\begin{gathered} h=2.25w+20 \\ where, \\ h=height\text{ of a small sunflower} \\ w=\text{ Number of weeks after it was planted} \end{gathered}$

- 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,

$\begin{gathered} \text{ Week 1:} \\ w=1, \\ h=2.25(1)+20 \\ h=2.25+20 \\ \\ \text{ Week 2:} \\ w=2, \\ h=2.25(2)+20 \\ h=4.5+20 \\ \\ \text{ Week 3:} \\ w=3, \\ h=2.25(3)+20 \\ h=6.75+20 \\ \\ And\text{ so on...} \end{gathered}$

- 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.

$\begin{gathered} h=2.25w+20 \\ w=0 \\ h=2.25(0)+20 \\ h=20 \end{gathered}$

- 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