In the 1860s and 1870s Nevada experienced a mining boom. Suppose population of a boom town can be modeled by the function where t is the number of years since 1860. What was the average population of the boom town between 1871 and 1881?
A) 3,692 people
B) 7,386 people
C) 7,076 people
D) 3,769 people
E) 8,869 people

Question

In the 1860s and 1870s Nevada experienced a mining boom. Suppose population of a boom town can be modeled by the function  where t is the number of years since 1860. What was the average population of the boom town between 1871 and 1881?
A) 3,692 people 
B) 7,386 people 
C) 7,076 people 
D) 3,769 people 
E) 8,869 people

Quizplus · Accepted Answer

To find the average population between 1871 and 1881, we need to find the population at the beginning and end of this time period, and then take the average.

Substituting t = 11 and t = 21 into the given function, we get:

P(11) = 11e^(0.1*11) = 3,732.09 
P(21) = 11e^(0.1*21) = 10,419.87

Taking the average of these two values, we get:

(3,732.09 + 10,419.87)/2 = 7,076.98

Rounding to the nearest whole number, we get an average population of approximately 7,077 people. Therefore, the best choice is C.

In the 1860s and 1870s Nevada Experienced a Mining Boom