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A stone step in a very old building was 18 centimeters tall when it was built. It wears down 1 centimeter...

A stone step in a very old building was 18 centimeters tall when it was built. It wears down 1 centimeter every 400 years. Two students wrote models for the height of the step, y, in centimeters.
Kai: y = 18 - 0.0025x, where x is the time since the step was built, in years
Lena: y = 18 - 0.25x, where x is the time since the step was built, in centuries
Today the step is 16.5 centimeters tall. Which statement is true?
Only Kai's model is correct, and it shows the step is 600 years old.
Only Lena's model is correct, and it shows the step is 6 years old.
Both models are correct, but they give different ages for the step: 600 years and 6 years.
Both models are correct, and both show the step is 600 years old.

Answer

To find the correct model, we need to determine the age of the step using both models and see which one matches the current height of 16.5 centimeters.

  1. Kai's Model: y = 18 - 0.0025x

Set y = 16.5 and solve for x:

16.5 = 18 - 0.0025x

0.0025x = 18 - 16.5

0.0025x = 1.5

x = 1.5 / 0.0025

x = 600

The step is 600 years old according to Kai's model.

  1. Lena's Model: y = 18 - 0.25x

Set y = 16.5 and solve for x:

16.5 = 18 - 0.25x

0.25x = 18 - 16.5

0.25x = 1.5

x = 1.5 / 0.25

x = 6

The step is 6 centuries old, which is 600 years, according to Lena's model.

Both models are correct, and both show the step is 600 years old.

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