Question

The altitude at which we boil an egg affects how long it takes for the egg to achieve perfect hardness. It takes 198 seconds to boil a perfect egg at the lowest place possible, the edge of the Dead Sea, which has an altitude of -418 meters. The highest place possible is the summit of Mount Everest, which has an altitude of 8848 meters. It takes 209 seconds to boil a perfect egg there.

T(a) models the time (in seconds) it takes to boil a perfect egg at an altitude of 'a' meters. Which number type is more appropriate for the domain of T?

Choose 1 answer:

(Choice A) A: Integers

(Choice B) B: Real numbers

What's the appropriate domain?

Choose 1 answer:

(Choice A, Checked) A: -418 ≤ a ≤ 8848

(Choice B) B: 198 ≤ a ≤ 209

Stuck? Use a hint.

Answer 1

The correct domain of the function modeling the time it takes to boil an egg at different altitudes is the range of real numbers from -418 to 8848. Real numbers better represent the continuum of possible altitudes between the lowest and highest points on Earth.

Step-by-step explanation:

When determining the domain of the function T(a), which models the time it takes to boil an egg at an altitude of 'a' meters, we have to consider the practical range of altitudes at which boiling can occur, from the lowest land point to the highest. Altitude can take on any value within this range, including fractions, so the real numbers are the most appropriate for the domain of T. The relevant domain is therefore A: -418 ≤ a ≤ 8848, reflecting the altitudes from the shore of the Dead Sea to the summit of Mount Everest.

It's necessary to understand that altitude influences the boiling point of water due to changes in atmospheric pressure. As altitude increases, atmospheric pressure decreases, leading to a lower boiling point. This means that at higher altitudes, such as Denver or Mount Everest, water boils at a lower temperature, affecting cooking times.