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

Correct option: fourth one -> y = 6(1/3)^x

Step-by-step explanation:

A decay curve is produced by an exponencial function with a rate lesser than 1 and greater than 0. This way, we have an exponencial function where the values of y decrease when the values of x increase.

The first equation is a linear equation.

The second and third equations are exponencial equations, but with a rate bigger than 1

The fourth equation is an exponencial equation with a rate lesser than 1 and greater than 0, so this equation will produce a decay curve.

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb