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3 years ago

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Which of the following are examples of exponential decay? select all that apply.

1 answer:

Katarina [22]3 years ago

5 0

B, C and D are exponential decay.

Half-lives are given by exponential function, and since they are decreasing, it is decay.
With the teams being eliminated, this is decay.
Bacteria can be represented by exponential functions, and it is decreasing.

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Solve for x. Show the equation you used and your work.

levacccp [35]

The value of X is 27.

To solve this problem, you have to write a proportion with the given information. This can be done because the sides on the left and right are proportional with the values on the bottom.

36 / 24 = x / 18
x = 27

5 0

3 years ago

Find a compact form for generating functions of the sequence 1, 8,27,... , k^3

pantera1 [17]

This sequence has generating function

$F(x)=\displaystyle\sum_{k\ge0}k^3x^k$

(if we include $k=0$ for a moment)

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k$

Take the derivative to get

$\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k$

$\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k$

Take the derivative again:

$\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k$

$\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k$

Take the derivative one more time:

$\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k$

$\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k$

so we have

$\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}$

5 0

3 years ago

I’m kind of lazy to answer this question can somebody answer this for me

kirill [66]

Answer:

everyone got 6 pieces

Step-by-step explanation:

do you actually need a explanation?

4 0

2 years ago

Read 2 more answers

which expression shows the result of applying the distributive property to 12 (5y + 4) ? A. 60y + 48 B. 5y + 48 C. 17y + 16 D. 6

PSYCHO15rus [73]

A because you just distribute the 12 to both

7 0

3 years ago

Read 2 more answers

The perimeter of a square is 2 feet. how many inches long is each side of the square?

Yuki888 [10]

Perimeter of a square=4*side length
2=4*side length
2/4=side length
.5 or 1/2=side length

Hope this helps!

4 0

3 years ago

Read 2 more answers