Population Growth The rate of growth $d P / d t$ of a population of bacteria is proportional to the square root of $t,$ where $P$ is the population size and $t$ is the time in days $(0 \leq t \leq 10) .$ That is,

$\frac{d P}{d t}=k \sqrt{t}$

The initial size of the population is $500 .$ After 1 day, the population has grown to $600 .$ Estimate the population after 7 days.

$100(7)^{\frac{7}{2}}+500$

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