a) On January 1 2000, the park estimated that they had 500 deer on their land. Two years later, they estimated that there were 550 deer on the land. Assume that the number of deer was changing exponentially, i.e. P(t)=ae^bt where P is the number of deer at year t, and a and b are parameters.Find the values of a and b.

b) On January 1, 2005, the park management determined that the deer population is growing too quickly. So they decided to cull 20 deer from the herd every year thereafter (starting from January 1, 2006). Assume that the growth rate of the deer population is the same as in (a). Determine the differential equation that governs this situation, and solve it. Assume t=0 for the year 2005.

c) On January 1, 2010, the park management felt that the deer population is still rampant. They decided to remove deer so that the instantaneous rate of decrease is 10% of the deer population. Determine the differential equation that governs this situation, and solve it. Assume t=0 for the year 2010.

I only able to do part (a), I got a = 500, b = 0.04765

b) On January 1, 2005, the park management determined that the deer population is growing too quickly. So they decided to cull 20 deer from the herd every year thereafter (starting from January 1, 2006). Assume that the growth rate of the deer population is the same as in (a). Determine the differential equation that governs this situation, and solve it. Assume t=0 for the year 2005.

c) On January 1, 2010, the park management felt that the deer population is still rampant. They decided to remove deer so that the instantaneous rate of decrease is 10% of the deer population. Determine the differential equation that governs this situation, and solve it. Assume t=0 for the year 2010.

I only able to do part (a), I got a = 500, b = 0.04765