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{}{}=. the constant of proportionality is feet per millimeter.

Explanation:

Step1: Calculate the constant of proportionality

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

Step2: Find the model length 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 length of the plastic model for a 1.8 - mm long fish is 9.9 ft. The constant of proportionality $k = 5.5$ ft/mm.