Question

Quadratic models are fit to historical population data for two different European countries: Finland and Slovakia. The population of Finland, in millions of people, is modeled by F(t) = -0.0001t squared + 0.0271t + 4.0986, where
t is the number of years since 1950. The population of Slovakia, in millions of people, is modeled by S(t) = -0.0004t squared + 0.00584t + 3.4862, where t is also the number of years since 1950.

Which statement best compares the projected populations of the two countries in the year 2035?

A.
About 12,000 more people will live in Finland than Slovakia.

B.
About 120,000 more people will live in Finland than Slovakia.

C.
About 120,000 more people will live in Slovakia than Finland.

D.
About 1.2 million more people will live in Slovakia than Finland.

Answer 1

Year 2035 corresponds to t = 2035 − 1950 = 85.

Using the intended models (note: the Slovakia linear term is likely 0.0584, not 0.00584):

F(85) = −0.0001(85^2) + 0.0271(85) + 4.0986 ≈ 5.6796 million
S(85) = −0.0004(85^2) + 0.0584(85) + 3.4862 ≈ 5.5596 million

Difference ≈ 5.6796 − 5.5596 = 0.1200 million ≈ 120,000 more people in Finland.

Answer: B. (If you use the 0.00584 coefficient as written, the difference would be about 4.59 million in Finland, so the problem likely has a typo.)