Question

The current population of Fun City is 21000 people. If the population of the city will double every 51 years then the population after 171 years would be

Answer 1

Answer:

The population of Fun City after 171 years would be 214563.

Step-by-step explanation:

The statement depicts a case of exponential growth, whose model is described below:

$p(t) = p_{o}\cdot r^{\frac{t}{T} }$ (1)

Where:

$p_{o}$ - Initial population, no unit.

$p(t)$ - Current population, no unit.

$r$ - Growth rate, no unit.

$t$ - Time, in years.

$T$ - Growth period, in years.

If we know that $p_{o} = 21000$, $r = 2$, $t = 171\,yr$ and $T = 51\,yr$, then the population of the city after 171 years is:

$p(t) = 21000\cdot 2^{\frac{171}{51} }$

$p(t) = 214563$

The population of Fun City after 171 years would be 214563.