The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Marco is studying the change in the amount of money in two accounts, A and B, over time.

The amount f(x), in dollars, in account A after x years is represented by the function below:

f(x) = 1,264(1.09)x

Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)

Part B: The table below shows the amount g(r), in dollars, of money in account B after r years:

r (number of years) 1 2 3 4
g(r) (amount in dollars) 1,375 1,512.50 1,663.75 1,830.13

Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer. (5 points)

A

Step-by-step explanation:

Account A: Decreasing at 8 % per year

Account B: Decreasing at 10.00 % per year

Account B shows the greater percentage change  

Step-by-step explanation:

Part A: Percent change from exponential formula

f(x) = 9628(0.92)ˣ

The general formula for an exponential function is

y = ab^x, where

b = the base of the exponential function.

if b < 1, we have an exponential decay function.

ƒ(x) decreases as x increases.

Account A is decreasing each year.

We can rewrite the formula for an exponential decay function as:

    y = a(1 – b)ˣ, where

1 – b = the decay factor

    b = the percent change in decimal form

If we compare the two formulas, we find

0.92 = 1 - b

b = 1 - 0.92 = 0.08  = 8 %

The account is decreasing at an annual rate of 8 %.

The account is decreasing at an annual rate of 10.00 %.

Account B recorded a greater percentage change in the amount of money over the previous year.

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!

is there supposed to be a diagram or a graph for this one? ?

step-by-step explanation: