Question

The gross domestic product, G, of Switzerland was 310 billion dollars in 2007. Give a formula for G (in billions of dollars) t years after 2007 if G increases by

a. 3% per year

b. 8 billion dollars per year.

Suppose that (a) holds. Determine the year when Switzerland's GDP reaches 410 billion dollars.

Answer 1

a. Initial value of G = 310 billion dollars

Rate of increase r = 3% = 0.03

Therefore,

Formula for G, t years after 2007 is given by

  

=>

=>

b. Initial value of G = 310 billion dollars

Rate of increase r = 8 billions dollars per year

Therefore,

  Formula for G, t years after 2007 is given by

G(t) = Initial Value + r * t

=> G(t) = 310 + 8t

Let us assume GDP reaches 410 billion dollars after n years

Therefore,

  

=>

=>

=> n ln (1.03) = ln (41 / 31)

=> n = ln (41 / 31) / ln (1.03)

=> n = 9.46

=> n 9

Therefore,

GDP reaches 410 billion dollars after 9 years i.e. in the year 2007 + 9 = 2016