Consider a population that begins growing exponentially at a base rate of

$4\mathrm{.}64\mathrm{.}6\%$

per year and then follows a logistic growth pattern. If the carrying capacity is

$6868$

$$million$,$ find the actual fractional growth when the population is at $10$ million, $30$ million, and $50$ million.

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Part $1$

The fractional growth rate is about

$2\mathrm{.}392\mathrm{.}39\%$

when the population is $10$ million.