# Carbon dating differential equation

Orthogonal trajectories, therefore, are two families of curves that always intersect perpendicularly.

A pair of intersecting curves will be perpendicular if the product of their slopes is −1, that is, if the slope of one is the negative reciprocal of the slope of the other.

The half-life of a radioactive isotope describes the amount carbon carbon that carbon takes half of the isotope in a sample to decay.

At high speeds, the strength of the air resistance force (the is a proportionality constant determined by such factors as the diver's cross‐sectional area and the viscosity of the air.

Once the parachute opens, the descent speed decreases greatly, and the strength of the air resistance force is given by stays constant.

However, as the object cools, the temperature difference gets smaller, and the cooling rate decreases; thus, the object cools more and more slowly as time passes.

To formulate this process mathematically, let Example 4: A cup of coffee (temperature = 190°F) is placed in a room whose temperature is 70°F.