Question

Sean began jogging to live a healthier lifestyle. On his first run, he ran one-half mile. He increased his workouts by adding two miles a month to his run. He wrote the equation f(x)= 0.5 + 2x to model his progress. The variable x represents the number of

Answer 1

x would represent the number of months he ran and added on to the mileages.

It is the month because are starting at 0.5 miles. Then we increase 2 miles every month. so it is 2x.

Answer 2

x is the number of months

Explanation:

On the first run, hence after 0 months, Sean ran 0.5 miles or

`0.5+2\cdot0 \quad \text{miles.}`

After 1 moth, Sean increased 2 miles to his run, hence during the first and second month, Sean ran 2.5 miles or

`0.5+2=0.5+2\cdot1 \quad \text{miles.}`

After 2 moths, Sean increased 2 miles more to his run, hence during the second and third month, Sean ran 4.5 miles or

`0.5+4=0.5+2+2=0.5+2\cdot2\quad\text{miles.}`

After 3 moths, Sean increased 2 miles more to his run, hence during the third and fourth month, Sean ran 6.5 miles or

`0.5+6=0.5+4+2=0.5+2+2+2=0.5+2\cdot3 \quad \text{miles.}`

Using the same rule, we see that after x-months Sean will run

`0.5+2\cdot x \quad \text{miles.}`