Question

The average number of traffic tickets issued in a city on any given day

Sunday-Saturday
can be approximated by

T(x) = -6x2 + 84x + 37

where x represents the number of days after Sunday (x = 0 represents Sunday, x = 1
represents Monday, etc.) and T(x) represents the number of traffic tickets issued.

a) On which day are the most tickets written?
(select)
b) How many tickets are issued on that day?​

Answer 1

The most tickets were written on Saturday .On Saturday 325 tickets were issued

Explanation:

The average number of traffic tickets issued in a city on any given day Sunday-Saturday can be approximated by

`T(x) = -6x^2 + 84x + 37`

Where x represents the number of days after Sunday

T(x) represents the number of traffic tickets issued.

Sunday = x=0

Monday = x=1

Tuesday = x=2

Wednesday = x=3

Thursday = x =4

Friday = x=5

Saturday = x=6

Substitute x= 0

`T(x) = -6x^2 + 84x + 37\\T(x) = -6(0)^2 + 84(0) + 37\\T(x)=37`

On Sunday 37 tickets were issued

Substitute x= 1

`T(x) = -6x^2 + 84x + 37\\T(x) = -6(1)^2 + 84(1) + 37\\T(x)=115`

On Monday 115 tickets were issued

Substitute x= 2

`T(x) = -6x^2 + 84x + 37\\T(x) = -6(2)^2 + 84(2) + 37\\T(x)=181`

On Tuesday 181 tickets were issued

Substitute x= 3

`T(x) = -6x^2 + 84x + 37\\T(x) = -6(3)^2 + 84(3) + 37\\T(x)=235`

On Wednesday 235 tickets were issued

Substitute x= 4

`T(x) = -6x^2 + 84x + 37\\T(x) = -6(4)^2 + 84(4) + 37\\T(x)=277`

On Thursday 277 tickets were issued

Substitute x= 5

`T(x) = -6x^2 + 84x + 37\\T(x) = -6(5)^2 + 84(5) + 37\\T(x)=307`

On Friday 307 tickets were issued

Substitute x= 6

`T(x) = -6x^2 + 84x + 37\\T(x) = -6(6)^2 + 84(6) + 37\\T(x)=325`

On Saturday 325 tickets were issued

Hence the most tickets were written on Saturday .On Saturday 325 tickets were issued