contestada

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?

Respuesta :

danielmaduroh

Answer:

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

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:

[tex]5.4-5=0.4mi[/tex]

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

[tex]6.2-5.4=0.8mi[/tex]

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

[tex]7.8-6.2=1.6mi[/tex]

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:

[tex]x_{5}-7.8=3.2mi \\ \\ x_{5}=7.8+3.2=11mi, \ \text{Day 5}[/tex]

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

[tex]x_{6}-11=6.4mi \\ \\ x_{6}=6.4+11=17.4mi, \ \text{Day 6}[/tex]

Finally:

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

[tex]x_{7}-17.4=12.8mi \\ \\ x_{7}=12.8+17.4=30.2mi, \ \text{Day 7}[/tex]

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