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 2010. Round your answer to the nearest human.
A) 149,182
B) 332,012
C) 222,554
D) 67,032
E) 44,933

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 2010. Round your answer to the nearest human. ​
A) ​149,182 
B) ​332,012 
C) ​222,554 
D) ​67,032 
E) ​44,933

Quizplus · Accepted Answer

Using the formula 11ea984b_adee_5c90_9029_cb064df25eb2_TB4005_11,
y = 100,000*e^(k*1990)
149,182 = 100,000*e^(k*2000)
Divide the second equation by the first and take the natural logarithm of both sides:
ln(149,182/100,000) = 10k
k = ln(149,182/100,000)/10 = 0.0433
So the formula becomes:
y = 100,000*e^(0.0433x), where x is the number of years after 1990.
To estimate the population in 2010, we plug in x = 20:
y = 100,000*e^(0.0433*20) = 222,554 (rounded to the nearest whole number)

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