A leaky balloon: we used a linear function to describe air leaking from a balloon, but we indicated there that this is not, in fact, an accurate description. Let’s look more carefully. Suppose a...

A leaky balloon: we used a linear function to describe air leaking from a balloon, but we indicated there that this is not, in fact, an accurate description. Let’s look more carefully. Suppose a balloon initially holds 2 liters of air. Let B = B(t) denote the volume, in liters, of air in the balloon t seconds after it starts leaking. When a balloon is almost full, the air pressure inside is large, so it leaks rapidly. When it is almost empty, it leaks more slowly. More formally, the rate of change in B is proportional to B. Assume that for this particular balloon, the constant of proportionality is −0.05.

a. Write an equation of change for B.

b. Find a formula for B.

c. How long will it take for half of the air to leak out of the balloon?