The Time in Days $t = 0$ ) Is 500 Write an Equation That Gives the Population at Any

Multiple Choice

$\text { Suppose a population of bacteria is changing at a rate of } \frac { d p } { d t } = \frac { 1,000 } { 1 + 0.5 t } \text {, where } t \text { is }$ the time in days. The initial population (when $t = 0$ ) is 500 . Write an equation that gives the population at any time $t$ .

A) $p ( t ) = 2,000 \ln | 1 + 0.5 t | + 250$
B) $p ( t ) = \ln | 1 + 0.5 t | + 500$
C) $p ( t ) = 1,000 \ln | 1 + 0.5 t | + 500$
D) $p ( t ) = 1,000 \ln | 1 + 0.5 t | + 250$
E) $p ( t ) = 2,000 \ln | 1 + 0.5 t | + 500$