Without graphing determine whether the function represents exponential growth or exponential decay. y=4(5/6)^x y=12(17/10)^x y=129(1.63)^x

Since 5/6 is less than 1, hence the exponential equation is an exponential decay

Since 1.7 is greater than 1, hence the exponential equation is an

exponential growth

Since 1.63 is greater than 1, hence the exponential equation is an exponential growth

The standard form of an exponential equation is

The value of "b" in the expression determines whether the exponential equation given is s decay or an exponential growth

For the exponential equation

Compared with the standard expression, we will see that b = 5/6

Since 5/6 is less than 1, hence the exponential equation is an exponential decay

Similarly for the exponential equation

Compared with the standard expression, we will see that b = 1.7

Since 1.7 is greater than 1, hence the exponential equation is an

exponential growth

Also,  for the exponential equation

Compared with the standard expression, we will see that b = 1.63

Since 1.63 is greater than 1, hence the exponential equation is an exponential growth

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answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

step-by-step explanation:

there are 36 inches in a yard

25 : 36 = 0.69 yards (you can round to 0.70)