It has been observed that a particular plant's growth is directly proportional to time. It measured 2 cm when it arrived at the nursery ang 2.5 cm exactly one week later. If the plant continues to grow at this rate, determine the function that represents the plant's growth. Thank you! :)

clearly the plant grows at 1/2 cm/week

So, you have a slope and a point (0,2)

...

To determine the function that represents the plant's growth, we first need to identify the relationship between the growth and time.

Given that the plant's growth is directly proportional to time, we can express this relationship using the form y = kx, where y represents the growth (in centimeters), x represents time (in weeks), and k represents the constant of proportionality.

Let's use the given information to find the value of k.

When the plant arrived at the nursery, it measured 2 cm. This corresponds to when time (x) is 0 weeks. Therefore, we have the following data point: (0, 2).

One week later, the plant measured 2.5 cm. This corresponds to when time (x) is 1 week. Therefore, we have another data point: (1, 2.5).

Now, we can use these data points to find the value of k.

Using the formula y = kx, and substituting in the coordinates of the first data point (0, 2), we get: 2 = k * 0. Solving for k, we find that k = 2.

With k = 2, we can write the function that represents the plant's growth as y = 2x.

Therefore, the function that represents the plant's growth is y = 2x, where y is the plant's growth in centimeters and x is the time in weeks.

To determine the function that represents the plant's growth, we can use the formula for a proportional relationship, which is y = kx, where y represents the dependent variable (in this case, the plant's growth), x represents the independent variable (in this case, time), and k is the constant of proportionality.

Given that the plant's growth is directly proportional to time, we can substitute the given values into the formula to find the constant of proportionality, k.

At time t = 0 (when it arrived at the nursery), the plant's growth is 2 cm. Therefore, we have the point (0, 2).

At time t = 1 week later, the plant's growth is 2.5 cm. Therefore, we have the point (1, 2.5).

Substituting these values into the formula, we can solve for k:

2 = k(0) --> 0 = k (since anything multiplied by 0 is 0)
2.5 = k(1) --> k = 2.5

Now that we have found the value of k, we can write the function that represents the plant's growth over time:

y = 2.5x

Therefore, the function that represents the plant's growth is y = 2.5x, where y is the plant's growth in cm and x is the time in weeks.