Aspy is trying to escape. she must get by four guards. each guard takes half of her remaining money. she then $64 for her plane ticket. how much money does she have to start with in order to make her escape?

The spy must have at the start the amount of $1,024 in order to escape

Step-by-step explanation:

Let

a ------> amount of money that the spy must have at the start to escape

y ----> the remaining money

x ----> the number of guards

In this problem the remaining money is going to be reduced by half, every time the spy passes through a guard, so we can use an exponential function of the form

where

a is the initial value (amount of money at the start)

b is the base

b=(1-r)

r is the rate of decay

In this problem we have

r=50% -----> r=0.50

The value of b is

b=(1-0.50)=0.50

substitute

we know that

In order to escape after the fourth guard the amount of money remaining must be equal to $64

so

For x=4, y=$64

substitute in the equation and solve for a

therefore

The spy must have at the start the amount of $1,024 in order to escape

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.