Ahive of bees contains 27 bees when it is first discovered. after 3 days, there are 36 bees. it is determined that the population of bees increases exponentially.
how many bees are will there be after 30 days?

Step-by-step explanation:

Givens

The population growth is modelled by the expression

Where is the population after days, is the initial population, is days and is the constant of proportionality.

Basically, in these kind of problems, we use the given information to find first

Now, with this constant, we find the population of bees after 30 days.

Therefore, after 30 days, there will be around 542 bees in the hive.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.