We are interested in measuring the pressure at different depths below the surface of the ocean. Pressure increases by approximately l atmosphere for every 10 m of depth below the surface (for example, at a depth of 20 m, there are approximately 3 atmospheres of pressure, 2 due the ocean and 1 to the atmosphere itself). Measuring a pressure of x atmospheres without crushing the device costs x2 dollars.
a. How much would it cost to measure the pressure 100 m down?
b. How much would it cost to measure the pressure 1000 m down?
c. How much would it cost to measure the pressure 5000 m down?
Scientifically, a quantity is large if it requires a tough measuring device to assess. In real life, toughness costs money. How much would it cost to measure the value in the above circumstances?