The population of Upper Anchora was 2,000,000 at the start of 1996 and was doubling every 10 years. How fast was it growing per year at the start of 1996? Round your answer to the nearest thousand.
A)138,000 people per year
B)129,000 people per year
C)139,000 people per year
D)140,000 people per year
E)278,000 people per year

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for exponential growth:

N = N0 * 2^(t/T)

where:

N = population at time t 
N0 = initial population 
t = time elapsed 
T = time it takes for the population to double

In this problem, we know that N0 = 2,000,000 and T = 10 years. We want to find the rate of population growth at the start of 1996, which is the same as finding the derivative of N with respect to t at t = 0.

dN/dt = (N0/T) * ln(2) * 2^(t/T)

Plugging in our values, we get:

dN/dt = (2,000,000/10) * ln(2) * 2^(0/10) 
dN/dt = 200,000 * ln(2) 
dN/dt ≈ 138,629

Rounding to the nearest thousand, we get:

dN/dt ≈ 139,000

Therefore, the answer is C) 139,000 people per year.

The Population of Upper Anchora Was 2,000,000 at the Start