Question

You bike

5
miles the first day of your​ training,
5.4 miles the second​ day,
6.2 miles the third​ day, and
7.8 miles the fourth day. If you continue this​ pattern, how many miles do you bike the seventh​ day?

Answer 1

You will bike 30.2 miles in the seventh day according to the prediction.

Step-by-step explanation:

Here we have the following data, You bike

• 5 miles the first day of your​ training,

• 5.4 miles the second​ day,

• 6.2 miles the third​ day, and

• 7.8 miles the fourth day.

So we can know some facts:

• From the first day to the second day the number of miles increases:

`5.4-5=0.4mi`

• From the second day to the third day the number of miles increases:

`6.2-5.4=0.8mi`

• From the third day to the fourth day the number of miles increases:

`7.8-6.2=1.6mi`

By taking a look at the pattern, we can see that each day you increases the number of miles by a factor of 2 compared to the previous day. So:

• From the fourth day to the fifth day the number of miles increases:

`x_(5)-7.8=3.2mi \\ \\ x_(5)=7.8+3.2=11mi, \ \text{Day 5}`

• From the fifth day to the sixth day the number of miles increases:

`x_(6)-11=6.4mi \\ \\ x_(6)=6.4+11=17.4mi, \ \text{Day 6}`

Finally:

• From the sixth day to the seventh day the number of miles increases:

`x_(7)-17.4=12.8mi \\ \\ x_(7)=12.8+17.4=30.2mi, \ \text{Day 7}`