The line of this graph shows the development regarding to the amount of individuals in a period of time. When the number of individuals rises as the time passes, the line should go up as well. And if the number of individuals decreases, the line should go down.
The carrying capacity refers to the number of individuals that a region can support without being harmed, and it is represented by the horizontal line that appears on all of the graphs. This means that when the line that shows the amount of individuals reaches this line, the space where those individuals live is on its maximum capacity.
So, regarding to this deer population, it rises until it reaches this point of carrying capacity, which means that the line showing the number of individuals will rise until it reaches the horizontal line. At this point, the population will stabilize, it won't grow too much or reduce itself too much, creating an S shape of small curves.
In graph A, the line of amount of individuals never stops rising, therefore it doesn't grow only until its carrying capacity is reached. Therefore, A is wrong.
Both graphs C and D shows lines that dowsn't make sense for the movement we're talking about. There's no way of even reading graph D as it shows a closed line. And graph C shows a population growing and decreasing repeatedly. So C and D are also incorrect.
Graph B shows exactly what was described. The line showing the number of individuals will rise until it reaches the horizontal line. At this point, the population will stabilize and the graph will show an S shape. Therefore, the correct answer is B.