The population y of a certain country was 100,000 in 1990 and 149,182 in 2000. Assume the formula applies to the growth of the country's population. Estimate the population of the country in 2005. Round your answer to the nearest human.
A)122,140
B)271,828
C)182,212
D)81,873
E)54,881

Question

The population y of a certain country was 100,000 in 1990 and 149,182 in 2000. Assume the formula  applies to the growth of the country's population. Estimate the population of the country in 2005. Round your answer to the nearest human. ​
A)122,140 
B)271,828 
C)182,212 
D)81,873 
E)54,881

Quizplus · Accepted Answer

Using the given formula, we can find the value of the constant k:
100,000 = 11e^(k*0)
149,182 = 11e^(k*10)
Dividing the second equation by the first, we get:
1.49182 = e^(10k)
Taking the natural logarithm of both sides:
ln(1.49182) = 10k
k = ln(1.49182)/10 ≈ 0.0433
Now we can use this value of k to estimate the population in 2005:
y = 11e^(0.0433*15) ≈ 182,212
Rounding to the nearest human, we get a population of 182,000, which corresponds to choice C.

The Population Y of a Certain Country Was 100,000 in 1990