3 The population of field mouse in a certain area is known to have an increase at a rate proportional to the present population. The initial population of the field mouse has doubled in 2 years (1). Determine the initial value problem (L. e., differential equation to- eether with initial condition) of describing the population of the tield mouse (Answer kP PO) h) (2). How long time will it take for the population of the field mouse to triple? (Answer 2tn3/In2 3.17 year) (3). Suppose that the population of the field mouse is 1,000 in 3 years, what was the initial population ( P(O)-P 1000 x23354) (4). Following part (2), Suppose that the population of the field mouse is 1,000 in 3 years, what will be the population in 6 years? Hint: First determine the population in t yeans PC)-1 2ir-3)/2 ( P(6) -1000 x 22828) (5). Following part (2), Suppose that the population of the field mouse is 1,000 in 3 years, how fast is the population growing in the 4th year? (Hint: Determine the increasing rate dP/dt at t4) ( 500V2 In 2 400 per year )