The population P (in thousands) of a colony of rabbits at time (t) years is given by P(t) = 5+ ae-bt. t>0 where a and b are positive constants. If it is given that the initial population is 10, 000 rabbits and one year later this population has reduced by 1,000, find the following; (a) The values of a and b. (b) The time (to 2 decimal places) when the population becomes two-thirds of the initial popu- lation. (c) The time when there is no change in the rabbit population as time changes. Explain your answer.

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.