Question

1) Louis just got his first job in a saving $45 a week he also has $155 see from his birthday that just passed Lewis came up with the following expression for the amount of savings 45w + 155 where w is the number of weeks that he has been saving.

According to this model, how much will Luis have saved after 6 weeks?

2) After a month, Louis noticed he had more than what his model above predicted due to the interest paid by the bank. Lewis adjusted his expression to now be w²/64 + 45w + 155

How much more will the second model predict to have saved in one year compared to the first mofel he came up with?​

Answer 1

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.