Australian glitter ants reproduce so that their population doubles every 15 days. If there are 3 ants initially, the equation is represented by y=3(2)^t/15, where t represents the number of days. Rewrite the equation in the form y=a(1+r)^t and find the daily increase rate represented by r.

  4.73%

Step-by-step explanation:

  y = 3×2^(t/15) = 3×(2^(1/15))^t = 3×1.0472941^t

In this form, ...

  1 +r = 1.0472941

  r = .0472941 ≈ 4.73%

The daily increase is about 4.73%.

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.

inverse operation of addition