Question

for her marine biology conference, jasmine uses a 3 - d printer to make plastic models of small fish she studies. the table shows the lengths of the actual fish compared to the lengths of plastic models. one fish is 1.8 millimeters long. find the length of the plastic model that depicts this fish. step 1: make an estimate. the model structure should be 9.9 feet long. step 2: find the constant of proportionality, k. k = \frac{square}{square}=square the constant of proportionality is square feet per millimeter. reset step

Explanation:

Step1: Calculate the constant of proportionality

The constant of proportionality $k$ is found by taking the ratio of the model length $y$ to the actual length $x$. Using the first - row values from the table ($x = 0.4$ mm and $y=2.2$ ft), $k=\frac{y}{x}=\frac{2.2}{0.4}=5.5$ ft/mm.

Step2: Find the length of the model for an actual length of 1.8 mm

We know that the relationship between the actual length $x$ and the model length $y$ is $y = kx$. Substituting $k = 5.5$ ft/mm and $x = 1.8$ mm, we get $y=5.5\times1.8 = 9.9$ ft.

Answer:

The constant of proportionality is $5.5$ feet per millimeter and the length of the plastic model for a 1.8 - mm long fish is $9.9$ feet.