Dylan just started a running plan where he runs 14 miles the first week and then increases the number of miles he runs by 10% each week. If he keeps up this plan for 11 weeks, how many total miles would Dylan have run, to the nearest whole number?

36 miles

Step-by-step explanation:

Given - Dylan just started a running plan where he runs 14 miles the first

            week and then increases the number of miles he runs by 10% each

            week.

To find - If he keeps up this plan for 11 weeks, how many total miles would  

              Dylan have run ?

Proof -

1st week = 14 miles

2nd week = 14 + 10% of 14 = 14 + 1.4 = 15.4

3rd week = 15.4 + 10% of 15.4 = 15.4 + 1.54 = 16.94

4th week = 16.94 + 10% of 16.94 = 16.94 + 1.694 = 18.634

5th week = 18.634 + 10% of 18.634 = 18.634 + 1.8634 = 20.4974

6th week = 20.4974 + 10% of 20.4974 = 20.4974 + 2.04974 = 22.54714

7th week = 22.54714 + 10% of 22.54714 = 22.54714 + 2.254714 = 24.801857

8th week = 24.801857  + 10% of 24.801857  = 24.801857  + 2.4801857  = 27.2820427

9th week = 27.2820427  + 10% of 27.2820427  = 27.2820427+ 2.72820427  = 30.01024697

10th week = 30.01024697  + 10% of 30.01024697  = 30.01024697 + 3.001024697  = 33.01127167

11th week = 33.01127167  + 10% of 33.01127167  = 33.01127167 + 3.301127167  = 36.31239884 ≈ 36

∴ we get

Total miles Dylan would run = 36 miles.  

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is