Chapter 6.1, Problem 42E

Population growth

42. The population of a community of foxes is observed to fluctuate on a 10-year cycle due to variations in the availability of prey. When population measurements began (t = 0), the population was 35 foxes. The growth rate in units of foxes/year was observed to be

$P^{\prime }(t)=5+10\sin \frac{\pi t}{5}.$

1. a. What is the population 15 years later? 35 years later?
2. b. Find the population P(t) at any time t ≥ 0.