In order to understand how the crew is being like this, let us first look at what the word “improvident” means. We will then see where Equiano uses it in the text and we will discuss how the word applies to that situation.
“Improvident” means something like “wasteful.” In particular, if you are improvident, you are not really thinking ahead. You are simply using things up or wasting them because you are not thinking about the idea that you might need them later. So, someone who spends all their money on clothes, not thinking about the fact that they need to pay rent later in the month, is improvident.
Now, let us see where Equiano uses this word. He uses it while discussing the way in which the slaves were jammed together in the hold of the ship. In this the quote from the book, Equiano says that the slaves were packed in so tightly and in such bad conditions that
…the air soon became unfit for respiration, from a variety of loathsome smells, and brought on a sickness among the slaves, of which many died, thus falling victims to the improvident avarice, as I may call it, of their purchasers.
So how is this improvident? Presumably, it is improvident because the crew is allowing the slaves to die. The fact that they are greedy (“avarice” is similar to greed) is shown by the fact that they are not willing to give slaves enough space in the ship. This is improvident because it is going to cause the slaves to die. If they die, the crew will not get any money for selling them. So, the crew is being greedy, but in a wasteful way that shows no foresight. They are cramming the slaves in as tightly as they can, not realizing that they could keep more slaves alive (and therefore get more money) if only they would give the slaves more space and better conditions.
So, the crew is being “improvident” because they are not thinking about the consequences of keeping the slaves in such terrible conditions. They are not thinking about how they could make more money by giving the slaves better conditions.