The Hippo Problem In order to hunt hippopotamuses, a hunter must have a hippopotamus-hunting license. Since Hakim the Hunter can sell the hippos he catches, he can use the proceeds to pay for part of or the entire license. If Hakim only catches three hippos, he is still $2050 in debt. If he catches seven hippos, he makes a profit of $1550. The African Game and Wildlife Commission allows a limit of ten hippos per hunter. A) What is the maximum amount of money Hakim can make? What is your evidence? B) What is the cost of the license? How do you know? C) What is the contextual meaning of the rate of change, y-intercept and x-intercept?

A) To find the maximum amount of money Hakim can make, we need to look at the scenario where he catches the maximum allowed hippos, which is ten. From the given information, we know that when Hakim catches seven hippos, he makes a profit of $1550. This means that for each additional hippo beyond seven, he makes a profit of $1550/3 = $516.67. So, for ten hippos, he would make a profit of $1550 + 3 * $516.67 = $2099.99. Therefore, the maximum amount of money Hakim can make is approximately $2100.

B) The cost of the license can be calculated by subtracting the debt Hakim is in when he catches three hippos from the debt when he catches seven hippos. When he catches three hippos, he is $2050 in debt, and when he catches seven hippos, he makes a profit of $1550. So, the cost of the license would be $2050 + $1550 = $3600.

C) The contextual meaning of the rate of change in this scenario would be how the profit or debt changes with each additional hippo caught. The y-intercept would represent the initial debt Hakim has before catching any hippos, and the x-intercept would represent the point at which Hakim breaks even (makes no profit or incurs no debt) by catching a certain number of hippos.

I hope this helps clarify the situation for you! If you have any more questions or need further explanation, feel free to ask.