Answer
a) In the year $2038$, Denmark's population will reach $6$ million.
b) In $236$ years, the population will double.
Work Step by Step
$P(t) = 5.5(1.00295)^{t}$
a)
$6 = 5.5(1.00295)^{t}$
$\frac{6}{5.5} = (1.00295)^{t}$
$t = \log_{1.00295} (\frac{6}{5.5})$
$t = \frac{\log (\frac{6}{5.5})}{\log (1.00295)}$
by GDC / calculator
$t = 29.5388...$ years
$t \approx 30$ years
$= 2008 + 30$
$= 2038$
b)
Double $= 5.5 \times 2 = 11$ million
$11 = 5.5(1.00295)^{t}$
$\frac{11}{5.5} = (1.00295)^{t}$
$2 = (1.00295)^{t}$
$t = \log_{1.00295} 2$
$t = \frac{\log 2 }{\log (1.00295)}$
by GDC / calculator
$t = 235.31154...$
$t \approx 236$ years
