In 1996 the deer population in a Pennsylvania county was 200

In 1996 the deer population in a Pennsylvania county was 20,000, and in 2000 it was 31,000. Assume the population growth exponentially. Use the formula n = n_0e^rt to find a function that models the deer population 1 years. Let t = 0 be the year 1996. What is the projected deer population in 2004? After how many years will the deer population reach 100,000? A culture starts with 8600 bacteria. After one hour the count is 10,000. Use the formula n = n_0e^rt to find a function that models the number of bacteria after t hours. Find the number of bacteria after 2 hours. After how many hours will the number of bacteria double?

Solution

44)a) 31000 = 20000*e^(r*4) ======> r = 0.1096

So model is n = no*e^(0.1096*t)

b) n = 20000*e^(0.1096*8) = 48063.94

c) 100000 = 20000*e^(0.1096*t) ============> t = 14.68 years

45) a) 10000 = 8600*e^(r*1) ======> r = 0.1508

So model is n = no*e^(0.1508*t)

b) n = 8600*e^(0.1508*2) = 11627.37

c) 2*8600 = 8600*e^(0.1508*t) ======> t = 4.6 hrs