write a rule to describe the function. After how many days will the zucchini plant be 0.25 meters tall?

Question

a zucchini plant in Darnell's garden was 9 centimeters tall when it was first planted. Since then, it has grown approximately 0.8 centI ethers per day.

Answer 1

Since the plant is growing at a constant rate, the relationship between time and the height of the plant is linear.  

 

Let x = number of days since planting

      y = height (in centimeters) on day x

 

When x = 0, y = 9

When x = 1, y = 9.8

 

Slope = (9.8 - 9)/(1-0) = 0.8

 

So, y = 0.8x + 9

 

0.25 meters = 25 cm

 

Find x so that y = 25:  0.8x + 9 = 25

 

                                               0.8x = 16

 

                                                    x = 20 days 

 

 

Answer 2

To start, notice they ASK FOR meters, but GIVE YOU centimeters. So you'll have to convert centimeters to meters first.

 

Centi- in Latin, means 100 so 1 meter = 100 centimeters and can also be written as the proportion: 1m/100cm

 

So, 9 centimeters is the same as .09 meters. And 0.8 centimeters is 0.008 meters (notice the trick of simple moving your decimal to the right 2 places).

 

Now, let's look at the problem. We know we started with a 9 centimeter tall plant. This is our constant, because it's not changing. We were then told we grown 0.008 meters per day. The 'per day' means this is a changing variable, thus we call it x. So, if we write the equation....

 

0.008x + 0.09 

 

Now we want to know when this will equal 0.25 meters. Therefore, we make what we just wrote equal to 0.25

 

0.25 = 0.008x + 0.09      now we solve for x... move 0.09 to the left (ie. subtract)

0.16 = 0.008x                 divide both sides by 0.008

20 = x

 

We now know that in 20 days, we'll be .25 meters tall. 

 

Optional: I personally do not like working with decimals. Another option to this problem is to convert 0.25 meters into centimeters (25cm) and do the same problem without all the decimals.

 

If you have any other questions or want to discuss this one further, please get a hold of me :)