Multiple choice

The population of a city increases at the rate of $4$% per year. If in time $t$, the population becomes $p$, then equation of $p$ in terms of $t$ is ______

  1. $p={ e }^{ \cfrac { t }{ 25 } }$
  2. $p=4.{ e }^{ \cfrac { t }{ 25 } }\quad $
  3. $p=c.{ e }^{ \cfrac { t }{ 25 } }$
  4. $p=\cfrac { 1 }{ 25 } { e }^{ 4t }$
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C Correct answer
Explanation

The growth follows the exponential model p = p0 * e^(rt). Given the rate is 4% per year, r = 0.04 = 1/25. Thus, p = c * e^(t/25), where c is the initial population.

AI explanation

The population growth follows the continuous compound interest formula p = p0 * e^(rt), where r is the rate of 0.04 and t is the time. Substituting the rate gives p = c * e^(0.04t), where c is the initial population. Since 0.04 is equivalent to the fraction 1/25, the equation can be written as p = c * e^(t/25).

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