CPM Homework Help : CALC Problem 7-156

Stingray populations grow based on the differential equation below, where $P$ is the population (in thousands) and $t$ is time in years. Use the graph of the slope field at right to answer the following questions.

$\frac { d P } { d t }= 0.026P(12.5 − P)$

If there are $3{,}000$ stingrays at time $t = 0$ , sketch a curve representing their population of stingrays.
Hint (a):
The starting point of the curve is ( $0$ , $3000$ ).

What if the original population at $t = 0$ is $10{,}000$ stingrays? Draw that population curve and decide if its growth is the same or different as that in part (a).
Hint (b):
The starting point of the curve is ( $0$ , $10{,}000$ ).
What if the original population at $t = 0$ is $17{,}000$ stingrays? Draw that population curve and decide if its growth is the same or different as those in parts (a) and (b).
Hint (c):
Based on parts (a) and (b), you should have noticed that both curves approached the same value over time. The starting point of this curve is ( $0$ , $17{,}000$ ). Do you think it will approach the same threshold?