A pond initially contains $1,000,000$gal of water and an unknown amount of an undesirable chemical. Water containing $0\mathrm{.}01$ g of this chemical per gallon flows into the pond at a rate of $320ga\frac{l}{h}r.$ The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. Let $q(t)$ represent the amount $($in grams$)$ of the chemical in the pond at any time.

a$.$ What is the concentration $($grams per gallon$)$ of the chemical in the pond at any time, in terms of $q?$

b$.$ How many grams of the chemical are pumped in per hour?

c$.$ How many grams of the chemical are pumped out per hour?

d$.$ Write a differential equation for the amount of the chemical in the pond at any time.

e$.$ How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially?