Answer:
42.25$ more saved.
Explanation:
Let's calculate the savings using both models:
Using the first model:
�
1
(
�
)
=
45
�
+
155
S
1
(w)=45w+155
After 6 weeks, Luis will have saved:
S_1(6) = 45 * 6 + 155 = 270 + 155 = $425
So, according to the first model, Luis will have saved $425 after 6 weeks.
Using the second model:
�
2
(
�
)
=
�
2
64
+
45
�
+
155
S
2
(w)=
64
w
2
+45w+155
To find out how much more the second model predicts Luis will have saved in one year (52 weeks) compared to the first model:
First, calculate the savings using the second model after 52 weeks:
�
2
(
52
)
=
5
2
2
64
+
45
∗
52
+
155
S
2
(52)=
64
52
2
+45∗52+155
Now, calculate the savings using the first model after 52 weeks (as already calculated in part 1):
�
1
(
52
)
=
45
∗
52
+
155
S
1
(52)=45∗52+155
Now, find the difference between the two models' predictions:
Difference
=
�
2
(
52
)
−
�
1
(
52
)
Difference=S
2
(52)−S
1
(52)
Calculate both values:
S_2(52) = \frac{2704}{64} + 2340 + 155 = 42.25 + 2340 + 155 = $2537.25
S_1(52) = 45 * 52 + 155 = 2340 + 155 = $2495
Now, find the difference:
{Difference} = 2537.25 - 2495 = $42.25
So, the second model predicts that Luis will have saved $42.25 more in one year compared to the first model.