### Home > MC2 > Chapter 11 > Lesson 11.1.1 > Problem11-6

11-6.

Anna kept track of the height of her fast-growing corn. Her records are shown in the table below.

 Day Height (cm) $0$ $2$ $4$ $6$ $8$ $x$ $2$ $7.5$ $13$ $18.5$ $24$
1. What is the growth rate of Anna's corn? Is this number always the same?

Find the difference in height of Anna's corn from day $0$ to day $2$ to find
how much her corn has grown in $2$ days.

$7.5 − 2 = 5.5$
Anna's corn grows $5.5$ cm every $2$ days.
To find how much Anna's corn grows in $1$ day, divide that number by $2$.

$\frac{5.5}{2} = 2.75$
The growth rate of Anna's corn is $2.75$ cm per day.

2. If you graph the points in this table, will they form a line or a curve? Explain how you know.

If the growth rate of Anna's corn is constant, as concluded from (a),
what would a graph with constant growth look like?

If you need more help, graph the points on graphing paper.
Let the number of days be on the x-axis and the height in centimeters be on the $y$-axis.

Since the rate of change is constant, the graph will form a line.

3. How would the growth rate show in the graph?

What would the graph look like if the number of days was on the
$x$-axis, while the height in centimeters was on the $y$-axis?

If the y-coordinate increases by $2.75$ for every day, the growth
rate will be represented by the slope of the line.

4. If Anna harvests the corn when it reaches $3$ meters, when will she harvest it?

$3$ meters is equivalent to how many centimeters?

$3$ meters is $300$ centimeters. When will the
height (the $y$-coordinate) reach $300$?

Find and use the rule to solve.