I have data: 

```
dat <- tibble(
         day = 200:210,
         x = sample(-10:10, size = 11,replace = T))

```

I have a variable `y` with initial value of 2. I want to calculate the final value of `y` by adding x to y in a given time step following 
the following notation: 

```
y[i] = y[i-1] + x

```

If I did this:

```
y <- 5
dat %>% mutate(y = y + x)

```

It adds y to each x. 

```
# A tibble: 11 x 3
    day     x     y
  <int> <int> <dbl>
1   200     4     9
2   201     3     8
3   202    -4     1
4   203    -7    -2
5   204    -3     2
6   205     1     6
7   206    -5     0
8   207    -1     4
9   208    -4     1
10  209    -2     3
11  210     4     9

The answer should be:

  # A tibble: 11 x 3
    day     x     y
  <int> <int> <dbl>
1   200     4     9
2   201     3     12
3   202    -4     8
4   203    -7     1
5   204    -3     -2
6   205     1     -1
7   206    -5     -6
8   207    -1     -7
9   208    -4     -11
10  209    -2     -13
11  210     4     -9

```

How do I achive this using dplyr package? Or any other method that is quick and fast. 

**EDIT**

If I want to impose a condition such that y cannot exceed 10 or be negative .If it exceeds 10, make it 10 and if it is negative, make it zero.
How do I achieve this:

A tibble: 11 x 3

```
      day     x     y     y1
  1   200     4     9     9
  2   201     3     12    10
  3   202    -4     8     6
  4   203    -7     1     0 
  5   204    -3     -2    0
  6   205     1     -1    0
  7   206    -5     -6    0
  8   207    -1     -7    0  
  9   208    -4     -11   0
  10  209    -2     -13   0
  11  210     4     -9    0

```