Final answer:
To estimate the population in 2006, we calculate the growth rate from the 1994 to 2001 data using the formula P = A · e^(kt), then apply this rate to estimate for 2006. We eliminate options that indicate no growth or reduction and infer that the correct answer is likely among the higher options provided.
Step-by-step explanation:
To estimate the population in 2006 using an exponential growth model, we need to apply the exponential growth formula P = A · e^(kt), where P is the future population, A is the initial population, e is the base of the natural logarithm, k is the growth rate, and t is the time in years.
First, we need to calculate the growth rate based on the population change from 85 million in 1994 to 89 million in 2001 (7 years).
Let A = 85 million (the population in 1994), and we have P = 89 million in t = 2001 - 1994 = 7 years.
Using the formula, 89 = 85 · e^(k·7), we can solve for k. Taking the natural logarithm of both sides gives us:
ln(89/85) = k·7
k = ln(89/85) / 7
Now that we have k, we can estimate the population in 2006 (t = 12 years since 1994), using the formula:
P = 85 · e^(k·12)
By plugging in the value for k that we calculated, we can then find the estimated population, rounding our answer to the nearest million.
The choices provided offer rounded numbers, which would approximate the calculated result using the given formula and known growth rate. Based on the growth pattern, it's unlikely that the population would reduce, therefore choices c (89 million) and d (85 million) can be eliminated. Between choices a (96 million) and b (92 million), we'd expect the population to have increased. Therefore, we can infer that the most appropriate estimate would be among these two values.