If a population of insects double each week and the initial number of the population is $500000$ if a predator kills $250000$ weekly what is the population function with respect to $t$ as $t$ with days.
What I tried the equation could be this $\frac{dp}{dt} = \frac{2t}{7} p - \frac{1}{7}(250000) $ ?? Or is it just $p(t) = (500000)2^{\frac{t}{7}} - \frac{t}{7} 250000$ Am I correct?
If you look at your equation and test it
$$ p(t) = (500000)2^{\frac{t}{7}} - \frac{t}{7}(250000) \tag{1} $$
At time $t=0$
$$ p(0) = (500000)2^{\frac{0}{7}} - \frac{0}{7}(250000) \\ 500000 \tag{2} $$
and in one week we have
$$ p(7) = 500000 \cdot 2 - \frac{7}{7} \cdot 250000 \\ = 750000 \tag{3} $$
Which is what we would expect, yes it is right.