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]
