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juin [17]
3 years ago
8

Suppose you invest $2000 at an annual interest rate of 4.5%. how long will it take for it to earn $495?

Mathematics
1 answer:
Neko [114]3 years ago
3 0
100%:2000$=4.5%:x$, x=90$. After 1st year I earned 90$, now I have 2090$.
100%:2090$=4.5%:x$, x=94.5$. After 2nd year I earned 94.5$ more, now I have 2184.05$.
100%:2184.05$=4.5%:x$, x=98.28$. After 3rd year I have 2282.33$.
100%:2282.33$=4.5%:x$, x=102.71$. After 4th year I have 2385.04$.
100%:2385.04$=4.5%:x$, x=107.33$. After 5th year I have 2492.37$.

So I need 6 years to earn 495$.
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Answer:

The graph of g(x) is wider.

Step-by-step explanation:

Parent function:

f(x)=x^2

New function:

g(x)=\left(\dfrac{1}{2}x\right)^2=\dfrac{1}{4}x^2

<u>Transformations</u>:

For a > 0

f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}

f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}

\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of}\:a\\ & \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\  & \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a\\\end{aligned}

\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a\\& \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a\\  & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a\\\end{aligned}

If the parent function is <u>shifted ¹/₄ unit up</u>:

\implies g(x)=x^2+\dfrac{1}{4}

If the parent function is <u>shifted ¹/₄ unit down</u>:

\implies g(x)=x^2-\dfrac{1}{4}

If the parent function is <u>compressed vertically</u> by a factor of ¹/₄:

\implies g(x)=\dfrac{1}{4}x^2

If the parent function is <u>stretched horizontally</u> by a factor of ¹/₂:

\implies g(x)=\left(\dfrac{1}{2}x\right)^2

Therefore, a vertical compression and a horizontal stretch mean that the graph of g(x) is wider.

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2 years ago
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Answer:

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Step-by-step explanation:

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