Which equation below will produce a decay curve y=2(4)^x y=3^x-4 y=6(1/3)^x y=1/2(3)^x

answer : y=6(1/3)^x, option C

Decay curve means when x value increases the y value will decrease.

We plug in 3 values for x and check the y value

Lets start with first option

x=0 , y= 2

x=1, y= 8

x=2, y=32

when x value increases the y value also increases. so option A is not a decay curve

x=0 , y= -4

x=1 , y= -1

x=2 , y = 5

when x value increases the y value also increases. so option B is not a decay curve.

x=0, y = 6

x=1, y = 2

x=2 , y= 0.67

when x value increases the y value decreases. so option C is a decay curve

step by step explanation: when u removing the parentheses and combined them that would be : x+3y-x-y=2y

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.