Suppose that the population (in millions)of Hungary in 2007 was 10 and that the expected continuous annual rate of change of the population is -0.003.Find the exponential growth model for the population by letting correspond to 2000.Round your answer to four decimal places.

Question

Suppose that the population (in millions)of Hungary in 2007 was 10 and that the expected continuous annual rate of change of the population is -0.003.Find the exponential growth model  for the population by letting  correspond to 2000.Round your answer to four decimal places. ​

Quizplus · Accepted Answer

We can use the exponential growth model:
P(t) = P0e^(rt)
where P0 is the initial population, r is the continuous annual rate of change, and t is the time in years. We can solve for the constant e using the fact that P(7) = 10 and r = -0.003:
10 = P0e^(-0.003*7)
10/P0 = e^(-0.021)
ln(10/P0) = -0.021
P0/10 = e^(0.021)
e = (P0/10)^(1/0.021)
Substituting P0 = 11eac44f_ecd4_063b_bedf_67bd5be74161_TB7497_11 (corresponding to 2000), we get:
e = (11eac44f_ecd4_063b_bedf_67bd5be74161_TB7497_11/10)^(1/0.021) ≈ 11eac44f_ecd4_2d4d_bedf_f790ca188dd9_TB7497_11
Therefore, the exponential growth model is:
P(t) = 11eac44f_ecd4_063b_bedf_67bd5be74161_TB7497_11*(11eac44f_ecd4_2d4d_bedf_f790ca188dd9_TB7497_11)^(t-2000)
Rounding to four decimal places, we get:
P(t) = 11eac44f_ecd4_2d4d_bedf_f790ca188dd9_TB7497_11*(11eac44f_ecd4_2d4e_bedf_fba584b6efee_TB7497_11)^(t-2000)

Suppose That the Population (In Millions)of Hungary in 2007 Was