Question

Determine the growth of plant a after 1 day .How does this compare to the growth of b?

Answer 1

Part 1

We have the graph of the growth of two plants A and B.

We have to compare the rate of growth of plant A and plant B.

Plant A, at day 1, has grown 0.5 mm. We can say that is having a rate of growth of 0.5 mm/day (NOTE: the average rate of growth can be calculated as the ratio of the growth and the number of days).

For plant B, it reachs 2/3 mm by day one. the rate of growth is 2/3 mm/day. This is approximately 0.67 mm/day.

We then know that Plant B grows faster than A by 0.67-0.5=0.17 mm/day.

Answer:

The true statement is "Plant B grows faster than Plant A. It grows 0.17 mm more per day.

Part 2

In order to test the proportionality we have to satisfy these two conditions:

- The center of coordinates (0,0) is part of the relationship. In this case, this is true for Plant A and Plant B, as the do not have any growth by day one.

- The slope (that is the value of the rate of growth in this case) has to be constant; that is, there is a linear relationship between the variables.

We can also test this mathematically: if y and x are proportional, y/x=k for any par (x,y), being k the constant of proportionality.

In the case of Plant A, we have y/x=0.5/1=0.5 and y/x=0.75/2=0.375. As the ratios give two different constant, the growth of Plant A is not proportional.

In the case of B, we have:

1/3 / 1/2 = 2/3

2/3 / 1 = 2/3

4/3 / 2 = 2/3

There is a constant of proportionality for the growth of Plant B, so the relation is proportional.

Answer:

"Plant A is non proportional because the points on the graph do not form a straight line. Plant B is proportional because there is a constant of proportionality between the days and the height measurements."

Part 3

We have a pool that is filled at a rate of 1000 gallons every 15 minutes.

The volume of the pool is 15,000 gallons.

We can write the relation between the volume and time as:

`V(t)=(1000)/(15)\cdot t`

They start filling the pool by 8 am, and Eva estimates the pool will be full by noon (12 pm), 4 hours from the starting time.

We can calculate the volume at 4 hours as (remember that t is in minutes):

`\begin{gathered} t=4\cdot60=240 \\ V(240)=(1000)/(15)\cdot240=(240,000)/(15)=16,000 \end{gathered}`

The pool will be filled before noon, as 16,000 gallons can be pumped in 4 hours.

We agree with Eva.