Question

A taxi service charges $1.00 for the first 1/10 of a mile and $0.10 for each additional 1/10 of a mile after that. fill in the table.

distance traveled

(miles)
9/10
2
3 1/10
10
price
?
(dollars)
Is this a proportional relationship?

Type yes or no

Answer 1

9414 1404 393

Answer:

$1.80, 2.90, 4.00, 10.90

not proportional

Explanation:

For some distance d, we have a charge f(d) that is ...

`f(d)=\begin{cases}1.00&0\le d\le0.1\\1.00+0.10\cdot((d-0.1))/(0.10)&0.1<d\end{cases}`

for d > 0.1, this simplifies to d +0.9.

Then the charges are ...

`\begin{array}{cc}\underline{\text{miles}}&\underline{\text{charge}}\\9/10&1.80\\2&2.90\\3\ 1/10&4.00\\10&10.90\end{array}`

The different relation for the first 1/10 mile indicates ...

the relationship is not proportional.