Your answer is partially correct.

The table below gives [tex]V=f(t)[/tex], the value in Canadian dollars (CAD) of [tex]$1[/tex] USD [tex]t[/tex] days after November 1, 2007. For instance, 1 USD could be traded for 0.9529 CAD on November 1.

[tex]\[
\begin{tabular}{c|c|c|c|c|c|c|c}
\hline
t & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
V & 0.9529 & 0.9463 & 0.9441 & 0.9350 & 0.9350 & 0.9349 & 0.9295 \\
\hline
\end{tabular}
\][/tex]

Evaluate each expression. Which gives the greater output value? Round your answers to five decimal places.

[tex]\[
\begin{array}{l}
\frac{f(4)-f(0)}{4-0}= \\
\frac{f(6)-f(4)}{6-4}=
\end{array}
\][/tex]

[tex]\square[/tex] [tex]\square[/tex]



Answer :

To analyze the given data and calculate the expressions, follow the steps below:

1. Understand the Data Table:
- The table lists the value in Canadian dollars (CAD) of 1 US dollar (USD) at different days after November 1, 2007.
- Specifically, for several values of [tex]\( t \)[/tex] (days), we have corresponding values of [tex]\( V \)[/tex] (CAD).

2. First Expression: [tex]\(\frac{f(4) - f(0)}{4 - 0}\)[/tex]
- Identify [tex]\( f(4) \)[/tex] and [tex]\( f(0) \)[/tex] from the table:
[tex]\[ f(4) = 0.9350 \quad \text{and} \quad f(0) = 0.9529 \][/tex]
- Substitute these values into the expression:
[tex]\[ \frac{f(4) - f(0)}{4 - 0} = \frac{0.9350 - 0.9529}{4 - 0} \][/tex]
- Simplify the numerator:
[tex]\[ 0.9350 - 0.9529 = -0.0179 \][/tex]
- Divide by 4:
[tex]\[ \frac{-0.0179}{4} = -0.004475 \][/tex]
- Round to five decimal places:
[tex]\[ -0.00448 \][/tex]

3. Second Expression: [tex]\(\frac{f(6) - f(4)}{6 - 4}\)[/tex]
- Identify [tex]\( f(6) \)[/tex] and [tex]\( f(4) \)[/tex] from the table:
[tex]\[ f(6) = 0.9295 \quad \text{and} \quad f(4) = 0.9350 \][/tex]
- Substitute these values into the expression:
[tex]\[ \frac{f(6) - f(4)}{6 - 4} = \frac{0.9295 - 0.9350}{6 - 4} \][/tex]
- Simplify the numerator:
[tex]\[ 0.9295 - 0.9350 = -0.0055 \][/tex]
- Divide by 2:
[tex]\[ \frac{-0.0055}{2} = -0.00275 \][/tex]
- Round to five decimal places:
[tex]\[ -0.00275 \][/tex]

4. Compare the Results:
- The first expression yields [tex]\(-0.00448\)[/tex] and the second expression yields [tex]\(-0.00275\)[/tex].
- Since [tex]\(-0.00275\)[/tex] is greater than [tex]\(-0.00448\)[/tex] (closer to zero),

The expression that gives the greater output value is:
[tex]\[ \frac{f(6) - f(4)}{6 - 4} = -0.00275 \][/tex]

Conclusively, the results are:
- [tex]\(\frac{f(4) - f(0)}{4 - 0} = -0.00448\)[/tex]
- [tex]\(\frac{f(6) - f(4)}{6 - 4} = -0.00275\)[/tex]