Question

uadratic 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
, where
is the number of years since 1950. The population of Slovakia, in millions of people, is modeled by
, where
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

I don’t see the two quadratic formulas in your message — can you paste them? (2035 corresponds to t = 2035 − 1950 = 85.)

How I’ll decide the answer once I have the formulas:
1. Evaluate each model at t = 85 to get the populations in millions: F(85) and S(85).
2. Compute the difference D = F(85) − S(85) (in millions).
3. Convert to number of people: people difference = D × 1,000,000.
4. Compare to the choices (in millions):
- A = 0.012 million (12,000)
- B = 0.12 million (120,000)
- C = −0.12 million (i.e. Slovakia 120,000 more)
- D = 1.2 million

Send the two quadratic models and I’ll evaluate and pick the correct choice.