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erastovalidia [21]
4 years ago
8

Y = 100 (1- 1/2) ^t decay or growth

Mathematics
1 answer:
charle [14.2K]4 years ago
8 0

Answer:

Decay

Step-by-step explanation:

We are given an equation y=100(1-0.5)^t

We need to say about decay or growth of exponential function.

Exponential function: y=a\cdot b^x

Where,

  • a is initial value of exponential function.
  • b is decay or growth of function

For decay: 0<b<1

For growth: b>1

Now we rewrite the equation into this form

y=100(1-0.5)^t

Changes to

y=100(0.5)^t

Here, b=0.5 < 1

Therefore, The given function would be decay.

Thus, y=100(1-0.5)^t is deacy.



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Step-by-step explanation:

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x=\frac{13+y}{5}

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Answer:

Part A

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f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.

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Part C

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Part D:

h(n)=1.1+0.4(n-1)\\h(n)=\left\{\begin{matrix}1.1 & if\:n=1 \\ h(n+1)+0.4 & if\:n\geq 2\end{matrix}\right

Step-by-step explanation:

By definition, an Arithmetic Sequence holds the same difference between each following number.

Part A

(52,40, 28, 16)\\52-40=12\\40-28=12\\28-16=12\\d=12

<u>Explicit Formula</u>

To write an explicit formula is to write it as function.

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<u>Recursive Formula</u>

To write it as recursive formula, is to write it as recurrence given to some restrictions:

f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.

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<u>Explicit formula</u>

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<u>Recursive Formula</u>

h(n)=\left\{\begin{matrix}1.1 &if\:n=1 \\ h(n+1)+0.4 &if\: n\geq 2\end{matrix}\right.

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