Consider a population of rabbits in a region with unlimited food resources. Suppose that the growth rate is proportional to the population with a proportionality factor of 4 per month, and every month we collect 3 rabbits. Then, the rabbit population is described by the differential equation
y′=4y−3.

a. Find an explicit expression of all solutions y of the differential equation above. Denote by c any arbitrary integration constant.
b. Suppose the initial rabbit population is 5. From all the solutions above, find the only solution that satisfies the initial condition y(0)=5

Drag and drop the answers into the boxes to complete this informal argument explaining how to derive the formula for the volume of a cone. since the volume of a cone is part of the volume of a cylinder with the same base and height, find the volume of a cylinder first. the base of a cylinder is a circle. the area of the base of a cylinder is , where r represents the radius. the volume of a cylinder can be described as slices of the base stacked upon each other. so, the volume of the cylinder can be found by multiplying the area of the circle by the height h of the cylinder. the volume of a cone is of the volume of a cylinder. therefore, the formula for the volume of a cone is 1/3 1/2 1/3πr^2h 1/2πr^2h πr^2h πr^2

The sum of the squares of two numbers is 8 . the product of the two numbers is 4. find the numbers.

James is playing his favorite game at the arcade. after playing the game 33 times, he has 88 tokens remaining. he initially had 2020 tokens, and the game costs the same number of tokens each time. the number tt of tokens james has is a function of gg, the number of games he plays