Question

The population size, in thousands, of a certain city can be modeled by the function P(t)= 268(1.02)^t, where t is the number of years after 2000 and t<_ 10. Which of the following statements best describes the change in the population size in the years between 2000
and 2010?


For each
-year period, the population of the city at the end of the period was approximately
greater than at the beginning of the period.

Option A,For each 1 -year period, the population of the city at the end of the period was approximately 2% greater than at the beginning of the period.

a

For each
-year period, the population of the city at the end of the period was approximately
greater than at the beginning of the period.

Option B,For each 1 -year period, the population of the city at the end of the period was approximately 10% greater than at the beginning of the period.

b

In the
-year period, the population of the city increased by a total of approximately
people.

Option C,In the 10 -year period, the population of the city increased by a total of approximately 20,000 people.

c

In the
-year period, the population of the city increased by a total of approximately
people.

Option D,In the 10 -year period, the population of the city increased by a total of approximately 53,600 people.

d

Answer 1

Option A.

Because P(t)=268(1.02)^t, the factor 1.02 means a 2% increase each year. (Over 10 years the population becomes 268(1.02)^10 ≈ 326.7 thousand, an increase of about 58.7 thousand, so the 20,000 and 53,600 figures are incorrect.)