Jacob is training for a marathon. His plan is to run the same distance for 3 days a week, then increase that distance by the same amount each week of training. During week 6, Jacob runs 14 miles per day, which is 1.5 miles more per day than he ran during week 5. Which equation represents the daily running distance, in miles, as a function of time, t, in weeks?

Given:
Week 6 = 14 miles
Week 5 = 1.5 miles less than week 6.

1.5 miles is the common difference.

Week 6 = 14 miles
Week 5 = 12.5 miles
Week 4 = 11 miles
Week 3 = 9.5 miles
Week 2 = 8 miles
Week 1 = 6.5 miles

f(t) = first term + common difference(t-1)
f(t) = 6.5 miles + 1.5 miles (t-1)

f(1) = 6.5 + 1.5(1-1)
f(1) = 6.5 miles

f(2) = 6.5 + 1.5(2-1)
f(2) = 6.5 + 1.5
f(2) = 8 miles

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ayoushivt ayoushivt · Answer 2 · 2022-06-27T07:33:14+02:00

The daily running distance, in miles, as a function of time, t, in weeks is

15+4.5t .

What is a Function ?

A function is a law that defines relation between a dependent variable and a independent variable.

It comes with a defined range and domain.

It is given that

Let jacob run x distance each day ,

First week he travels 3x .

The distance which he increases every week is given by d ,

Then the distance travelled for each week t is given by

3x + (t-1)d

The distance travelled in 6th week is

3x +5d

It is given that

During week 6, Jacob runs 14 miles per day, 14*3 = 42

3x+5d = 42

which is 1.5 miles more per day than he ran during week 5.

1.5*3 = 4.5 more for the week

The distance travelled in 6th week is 3x+4d

3x+4d +4.5 = 3x+5d

d = 4.5 miles.

3x +5 *4.5 = 42

x = 6.5 miles.

The daily running distance, in miles, as a function of time, t, in weeks is 3x + (t-1)d

=19.5 +(t-1) *4.5

=19.5-4.5 +4.5t

=15+4.5t

To know more about Function

https://brainly.com/question/21145944

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