The differential equation in Example 3 of Section 2.1 is a well-known population model. Suppose the DE is changed to dP dt = P(a
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Did the calculations myself, probably too late for these to be of any use but I'll leaave them here anyways for anyone else that needs it in the future. Love yall!
a quick clarification and then some.
Profit is what's leftover after the cost is subtracted from the revenue, or namely, if you sell a product for some amount, say 10, and you sold 100 of those, so you made 10*100 or 1000, that's the revenue or the income coming in, however, in making the product you had to cover some expenses, like if it's clothing, well, you have to buy the garment and saw it, have premises and machines to make the clothing and so on, all that's expenses, and since it's out of pocket money, is Cost, if you subtract that Cost from the 1000 in Revenue, what's leftover, that surplus is Profit.
this company sells "p" units, each at $855, so their Revenue will just be 855p, expenses or Cost is a fixed amount of $6780, so the profit comes from their difference.
on a given month, they sold 250, namely p = 250, so their Revenue is just 250*855 = 213750 bucks, however, we need to remove the Costs of 6780, 213750 - 6780 = 206970, that's our Profit.
now, the CEO takes a bite of 15% of that