Question

Emily's lawn grows at a constant rate. The height of her lawn, during a 10-day period, is represented by the graph below.

The graph titled 'Emily's Lawn growth' shows 'Days since mowing' from 0 to 10 along the x axis and 'height of grass in centimeters’ from 0 to 10 along the y-axis. A solid line starts from (0, 4) and passes through (2, 5), and (4, 6).

Based on the graph, after how many days will the lawn be 12 centimeters in height?

A.
16 days


B.
24 days


C.
10 days


D.
8 days

Answer 1

To determine how many days it will take for Emily's lawn to reach a height of 12 centimeters, we first need to find the rate of growth of the lawn.

From the graph, we see the following points:
- At day 0, the height is 4 cm.
- At day 2, the height is 5 cm.
- At day 4, the height is 6 cm.

We can calculate the growth rate by finding the change in height over the change in days:

From day 0 to day 4 (which is a span of 4 days):
- The height increases from 4 cm to 6 cm, which is a change of 2 cm.

Thus, the growth rate is:
\[
\text{Growth Rate} = \frac{\text{Change in height}}{\text{Change in days}} = \frac{2 \, \text{cm}}{4 \, \text{days}} = 0.5 \, \text{cm/day}
\]

Now, we can express the height of the lawn as a function of time \(t\):
\[
\text{Height} = \text{Initial height} + \text{Growth rate} \times t
\]
Using \(4\) cm as the initial height:
\[
\text{Height} = 4 + 0.5t
\]

We want to find \(t\) when the height is 12 cm:
\[
12 = 4 + 0.5t
\]
Subtracting 4 from both sides:
\[
8 = 0.5t
\]
Now, multiplying both sides by 2:
\[
t = 16 \, \text{days}
\]

Therefore, the lawn will reach 12 centimeters in height after **16 days**.

The answer is **A. 16 days**.