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the picture shows the graphing numbers here are the questions: b. how much does the investment grow every year?c. how much money did the investment start out as?d. what sequence equation would represent this graph?e. hat would the value of the investment be after another 10 years?f. what would the value of the investment be after a total of 20 years.

The Picture Shows The Graphing Numbers Here Are The Questions B How Much Does The Investment Grow Every Yearc How Much Money Did The Investment Start Out Asd Wh class=

Sagot :

Part b) the trick consists of noting that the difference between the investment of any two consecutive years is the same: $1,750. (In general, this kind of table is called an arithmetic sequence). How much does the investment grow every year? Exactly $1,750.

Part c) The idea here is to find the "first term", which is the investment when everything began (first year): $20,000. (this could seem trivial, but it will be important).

Part d) Remember I told you that this kind of table is called arithmetic sequence (a_n). This means that they have the general (generic) form:

[tex]a_n=\text{ initial value}+(n-1)\cdot\text{ (growing rate)}[/tex]

By part b and c, our initial value is $20,000 and our growing rate is $1,750. So we get

[tex]a_n=20000+(n-1)\cdot1750[/tex]

Comment: You can think that those dates (initial term, and growing rate) are all you need to understand this kind of table.

Part e) This type of question reveals the "power" of the formula we obtained above (now we can make projections regarding the future; namely, beyond the table).

Now, there is a detail to keep in mind; the wording "another 10 years". It means we must find the value of the sequence in 15, not 10.

[tex]a_{15}=20000+(15-1)\cdot1750=44500[/tex]

Part f) Here there is no trick; we just need to calculate the 20th term of the sequence:

[tex]a_{20}=20000+(20-1)\cdot1750=53250[/tex]

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