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The function [tex]$V(n)$[/tex] represents the value of an investment (in thousands of dollars) after [tex]$n$[/tex] months.

[tex]\[
\begin{tabular}{|c|r|r|r|r|r|r|r|}
\hline
$n$ & 2 & 3 & 7 & 12 & 14 & 19 & 25 \\
\hline
$V(n)$ & 12 & 12.7 & 15.5 & 19 & 20.4 & 23.9 & 28.1 \\
\hline
\end{tabular}
\][/tex]

a. Write a sentence explaining the meaning of the statement [tex]$V(19)=23.9$[/tex] in the context of the problem.
The value of this investment is [tex]$\square$[/tex] dollars after [tex]$\square$[/tex] months.

b. Determine [tex]$V(3)$[/tex] and write a sentence explaining the meaning of your answer.
The value of this investment is [tex]$\square$[/tex] dollars after [tex]$\square$[/tex] months.

c. Determine [tex]$n$[/tex] when [tex]$V(n)=12$[/tex] and write a sentence explaining the meaning of your answer.
The value of this investment is [tex]$\square$[/tex] dollars after [tex]$\square$[/tex] months.

Sagot :

GinnyAnsweridn
Let's analyze the problem step-by-step using the information provided in the table and determine the meaning of each statement.

### Part (a):
Given:
[tex]\[ V(19) = 23.9 \][/tex]

To interpret this:
- [tex]\( V(19) = 23.9 \)[/tex] means that when [tex]\( n = 19 \)[/tex] months, the value of the investment is 23.9 thousand dollars.

Complete Sentence:
The value of this investment is 23.9 thousand dollars after 19 months.

### Part (b):
From the table:
[tex]\[ V(3) = 12.7 \][/tex]

To interpret this:
- [tex]\( V(3) = 12.7 \)[/tex] means that when [tex]\( n = 3 \)[/tex] months, the value of the investment is 12.7 thousand dollars.

Complete Sentence:
The value of this investment is 12.7 thousand dollars after 3 months.

### Part (c):
From the table, we need to find [tex]\( n \)[/tex] such that [tex]\( V(n) = 12 \)[/tex]:
[tex]\[ V(2) = 12 \][/tex]

To interpret this:
- [tex]\( V(2) = 12 \)[/tex] means that when [tex]\( n = 2 \)[/tex] months, the value of the investment is 12 thousand dollars.

Complete Sentence:
The value of this investment is 12 thousand dollars after 2 months.

Combining all the parts together, we have:
- (a) The value of this investment is 23.9 thousand dollars after 19 months.
- (b) The value of this investment is 12.7 thousand dollars after 3 months.
- (c) The value of this investment is 12 thouand dollars after 2 months.
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