Need help w math question

y = P • (1+r)^t

Balance after 2 years: $3307.5

Step-by-step explanation:

To answer this question, we will use standard equation that calculates bank interests:

A = P(1+(r/n))^(n•t)

It might seem complicated, but let's explain:

A - amount of money after the time period

P - principal amount, the amount of money you started with

r - interest rate, in decimal numbers

n - number of times interest is being calculated per year

t - number of years

Since here, interest is annual, n = 1, so our equation is:

A = P(1+r)^t

P = $3000

r = 5% = 0.05

t = 2 years

A = 3000(1+0.05)^2

A = 3000•(1.05)^2

A = $3307.5

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!