Set \( P(t) = 100000 = 50000 \cdot e^{0.03t} \)
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- Only positive value: \( x = 2 + 2\sqrt{5} \)
- #### \( 2 + 2\sqrt{5} \)
- The population of a city grows exponentially according to \( P(t) = 50000 \cdot e^{0.03t} \), where \( t \) is in years. How long will it take for the population to double?
- \( 2 = e^{0.03t} \)
- Take natural log: \( \ln 2 = 0.03t \)
- \( t = \frac{\ln 2}{0.03} \approx \frac{0.693}{0.03} \approx 23.1 \) years
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