Multiple choice

It has been observed that the population of a city has been increasing exponentially at the rate of 5% per year for past 5 decades and the same trend is expected to continue. If the population was 10 million in the year 2000, by when can it be expected to touch the 15 million mark? (The exponential model is y = y0eat, take loge1.5 = 0.4054)

  1. After 8.11 years

  2. After 12.12 years

  3. After 20 years

  4. After 23.15 years
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A Correct answer
Explanation

y = y0 * e^(at). 15 = 10 * e^(0.05 * t). 1.5 = e^(0.05 * t). ln(1.5) = 0.05 * t. 0.4054 = 0.05 * t. t = 0.4054 / 0.05 = 8.108 years.

AI explanation

Using the continuous exponential growth model y = y0 * e^(at) where y0 is 10 and the continuous rate a is 0.05, we set the equation 15 = 10 * e^(0.05t). This simplifies to 1.5 = e^(0.05t). Taking the natural logarithm of both sides yields 0.4054 = 0.05t, which gives t = 8.11 years.

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