The function f(x) = 50(0.952)x, where x is the time in years, models a declining feral cat population. How many feral cats will there be in 9 years?

Work Shown:

f(x) = 50(0.952)^x

f(9) = 50(0.952)^9

f(9) = 32.1146016801717

f(9) = 32 approximately

Side note: the exponential function is in the form a*b^x with b = 1+r = 0.952, which solves to r = -0.048. The negative r value means we have a 4.8% decrease each year.

Another note: you don't even need to use math to answer this question. Note how 50 is the starting population and the population is declining. Only choice B has a value smaller than 50, so we can rule out the others right away.

  32

Step-by-step explanation:

The initial value of the population is f(0) = 50(0.952^0) = 50. If the population is declining, it must be less than 50 in 9 years. The only answer choice that is less than 50 is ...

  about 32 feral cats

You can evaluate f(9) to choose the same

  f(9) = 50(0.952^9) ≈ 32.114 ≈ 32

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.

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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