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
, 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 — could you paste them? I need the explicit models to compute the 2035 populations.

If you want to do it yourself, here are the steps:

1. Let t = 2035 − 1950 = 85.
2. Evaluate the Finland model F(t) at t = 85 to get F(85) (this will be in millions).
3. Evaluate the Slovakia model S(t) at t = 85 to get S(85) (millions).
4. Compute the difference D = F(85) − S(85).
- If D > 0, Finland has D million more people; if D < 0, Slovakia has |D| million more.
5. Convert to people by multiplying by 1,000,000.
- 0.012 million = 12,000 people (option A)
- 0.12 million = 120,000 people (options B or C depending on sign)
- 1.2 million = 1,200,000 people (option D)

Paste the two quadratic functions and I’ll compute the correct choice.