# Chapter 6 - Logarithmic Functions - 6.5 Solving Exponential Equations - 6.5 Exercises - Page 527: 36

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

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