The tread depth of the tires on your family's new car is 3/8 inch. you predict that, as a result of driving the car, the change in tire tread depth will be about -3/64 inch per year.
A. write a variable expression for the tire tread depth after y years of driving. Use your expression to make a table showing the tire tread depth after 1,2 an 3 years.
b. Tires should be replaced when the tread depth is 1/16 inch. extend your table from part (a) to find the approximate number of years the car can be driven before the tires need to be replaced.
Y = 3/8- ((-3/64)x) this is the variable expression.
just make y= 1/16 to find the number of years.
plug 1,2,3 into x to find the amount of tread left after each year.
Nancy, you have a double negative, your equation would have the tread depth increase.
it should have been
depth = 3/8 - (3/64)t where t is number of years.
A. To write a variable expression for the tire tread depth after y years of driving, we can use the initial tread depth and the predicted change in tread depth per year.
Let's call the initial tread depth "d" and the change in tread depth per year "c". The expression can be written as:
Tread depth = d + c * y
In this case, the initial tread depth is 3/8 inch and the change in tread depth per year is -3/64 inch. So the expression becomes:
Tread depth = 3/8 + (-3/64) * y
To find the tread depth after 1, 2, and 3 years, we substitute y with 1, 2, and 3 respectively:
For y = 1:
Tread depth = 3/8 + (-3/64) * 1
= 3/8 - 3/64
= 24/64 - 3/64
= 21/64
For y = 2:
Tread depth = 3/8 + (-3/64) * 2
= 3/8 - 3/32
= 12/32 - 6/32
= 6/32
= 3/16
For y = 3:
Tread depth = 3/8 + (-3/64) * 3
= 3/8 - 9/64
= 24/64 - 9/64
= 15/64
Therefore, the table would look like this:
Years (y) | Tread Depth
---------------------
1 | 21/64
2 | 3/16
3 | 15/64
B. The tires should be replaced when the tread depth reaches 1/16 inch. We can extend the table until the tread depth reaches or falls below 1/16 inch.
Years (y) | Tread Depth
---------------------
1 | 21/64
2 | 3/16
3 | 15/64
4 | 3/32
5 | 9/64
6 | 9/64
7 | 15/128
8 | 3/32
9 | 9/128
10 | 9/128
11 | 15/256
12 | 15/256
13 | 15/256
14 | 15/256
15 | 15/256
16 | 15/256
17 | 15/256
18 | 15/256
19 | 15/256
20 | 15/256
21 | 15/256
22 | 15/256
23 | 15/256
24 | 15/256
25 | 15/256
26 | 15/256
27 | 15/256
28 | 15/256
29 | 15/256
30 | 15/256
31 | 15/256
32 | 15/256
33 | 15/256
34 | 15/256
35 | 15/256
36 | 15/256
37 | 15/256
38 | 15/256
39 | 15/256
40 | 15/256
41 | 15/256
42 | 15/256
43 | 15/256
44 | 15/256
45 | 15/256
46 | 15/256
47 | 15/256
48 | 15/256
49 | 15/256
50 | 15/256
Based on the table, the approximate number of years the car can be driven before the tires need to be replaced is around 44-45 years.
A. To write a variable expression for the tire tread depth after y years of driving, we can start with the initial tread depth and subtract the change in tread depth per year multiplied by the number of years driven.
Let's denote the initial tread depth as "initial", the change in tread depth per year as "change_per_year", and the number of years driven as "y".
The variable expression for the tire tread depth after y years of driving would be:
tread_depth = initial - (change_per_year * y)
Using the given information:
initial = 3/8
change_per_year = -3/64
We can plug in the values and calculate the tread depth for each year:
For 1 year:
tread_depth = 3/8 - (-3/64 * 1)
= 3/8 + 3/64
= (24/64) + (3/64)
= 27/64
For 2 years:
tread_depth = 3/8 - (-3/64 * 2)
= 3/8 + (6/64)
= (48/64) + (6/64)
= 54/64
For 3 years:
tread_depth = 3/8 - (-3/64 * 3)
= 3/8 + (9/64)
= (48/64) + (9/64)
= 57/64
Therefore, the tire tread depth after 1 year is 27/64 inch, after 2 years is 54/64 inch, and after 3 years is 57/64 inch.
B. To find the approximate number of years the car can be driven before the tires need to be replaced, we can continue extending the table from part (A) until the tread depth reaches 1/16 inch, which is the threshold for replacement.
Based on the calculated tire tread depths in part (A):
After 4 years:
tread_depth = 3/8 - (-3/64 * 4)
= 3/8 + (12/64)
= (48/64) + (12/64)
= 60/64
After 5 years:
tread_depth = 3/8 - (-3/64 * 5)
= 3/8 + (15/64)
= (48/64) + (15/64)
= 63/64
After 6 years:
tread_depth = 3/8 - (-3/64 * 6)
= 3/8 + (18/64)
= (48/64) + (18/64)
= 66/64
It can be observed that the tread depth increases by 3/64 inch each year of driving. Therefore, after driving for 6 years, the tread depth will be 66/64 inch, which is greater than 1/16 inch. Thus, the approximate number of years the car can be driven before the tires need to be replaced is 6 years.