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Cloud [144]
3 years ago
15

Samantha puts an initial $500 into a savings account. The account has a 4% annual compound interest rate. What is the function t

hat best represents Samantha's account and how much does she have in savings after 5 years? Round your answer to the nearest dollar. Hint: Use the formula, f(x) = P(1 r)x.
Mathematics
1 answer:
Licemer1 [7]3 years ago
5 0
I use a bit of a different looking formula.

A(t)=P(1+r/n)^nt

P=amount of money. (500)
r= rate (in decimal. 4%=0.04)
n=number of times per year (1 in this problem)
t=amount of time. (5 years)

Plugged in it looks like this:

A(t)=500 (1+ 0.04/1)^1x5

Then I put it into my calculator like this:

0.04/1+ 0.04

Then add one to the above answer:

0.04+1=1.04

Then raise the above answer to the 1x5:

1.04^5=1.2166......

Then multiply the above answer by 500:

1.2166.... x 500=608.3264512

She has $608 after 5 years.

Hope this helps, let me know if you have any questions.
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\bf \qquad \qquad \qquad \qquad \textit{function transformations}&#10;\\ \quad \\\\&#10;&#10;\begin{array}{rllll} &#10;% left side templates&#10;f(x)=&{{  A}}({{  B}}x+{{  C}})+{{  D}}&#10;\\ \quad \\&#10;y=&{{  A}}({{  B}}x+{{  C}})+{{  D}}&#10;\\ \quad \\&#10;f(x)=&{{  A}}\sqrt{{{  B}}x+{{  C}}}+{{  D}}&#10;\\ \quad \\&#10;f(x)=&{{  A}}(\mathbb{R})^{{{  B}}x+{{  C}}}+{{  D}}&#10;\\ \quad \\&#10;f(x)=&{{  A}} sin\left({{ B }}x+{{  C}}  \right)+{{  D}}&#10;\end{array}

\bf \begin{array}{llll}&#10;% right side info&#10;\bullet \textit{ stretches or shrinks horizontally by  } {{  A}}\cdot {{  B}}\\\\&#10;\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}&#10;\\\\&#10;\bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\&#10;\qquad  if\ \frac{{{  C}}}{{{  B}}}\textit{ is negative, to the right}\\\\&#10;\qquad  if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\\\&#10;\end{array}

\bf \begin{array}{llll}&#10;&#10;&#10;\bullet \textit{ vertical shift by }{{  D}}\\&#10;\qquad if\ {{  D}}\textit{ is negative, downwards}\\\\&#10;\qquad if\ {{  D}}\textit{ is positive, upwards}\\\\&#10;\bullet \textit{ period of }\frac{2\pi }{{{  B}}}&#10;\end{array}

now, with that template in mind, let's take a peek at this function

\bf \begin{array}{lllcclll}&#10;y=&2(&1x&-2)^2&-4\\&#10;&\uparrow &\uparrow &\uparrow &\uparrow \\&#10;&A&B&C&D&#10;\end{array}\\\\&#10;-----------------------------\\\\&#10;A\cdot B=2\impliedby \textit{shrunk by a factor of 2, of half-size}\\\\&#10;\cfrac{C}{B}= \cfrac{-2}{1}\implies -2\impliedby \textit{horizontal right shift of 2 units}\\\\&#10;D=-4\impliedby \textit{vertical down shift of 4 units}

so, the graph of y=2(x-2)²-4, is really the same graph of y=x², BUT, narrower, and moved about horizontally and vertically
8 0
3 years ago
Read 2 more answers
I need help with this
Harlamova29_29 [7]

Answer:

50 degrees.

Step-by-step explanation:

The three angles make up a straight line angle which = 180 degrees, so:

C = 180 - 65 - 65

= 50 degrees.

7 0
2 years ago
Read 2 more answers
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