d) The population of a village was 564 in 2000. Assume that population growth is represented by $P = 564e^{0.1t}$ where P is the number of people in the village at time t. i) When will the population be 5000 people? ii) In order to plan ahead, the mayor of the village would like to know what the population will be in the future. What would you predict the population to be in 2050? iii) What will the population be in 2050 if population growth is represented by $P = 564e^{0.15t}$ instead? [30 marks]
Added by Eric L.
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564e^t = 5000 Divide both sides by 564: e^t = 5000/564 Take the natural logarithm of both sides: ln(e^t) = ln(5000/564) t = ln(5000/564) Using a calculator, we find that t ≈ 2.68 years. So, the population will be 5000 people in approximately 2.68 years. Show more…
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