Question

an athlete is training to run a marathon. she plans to run 2 miles the first week. she increases the distance by 8% each week. which function models how far she will run in the nth week?

Answer 1

Pls tell me I'm having a quiz with my teacher


P.S.= She is really evil

Answer 2

She will run 2 miles first week.

Second week she will run 2 miles + extra 8%:
first_week + 8%*first_week

Third week she will run same distance as in second + extra 8% above what she ran in second week:
second_week + 8%*second_week

Fourth week she will run same distance as in third + extra 8% above what she ran in third week:
third_week + 8%*third week

By taking out common factors we get:
Week 1: 1*2 miles
Week 2: (1+0.08) * week1
Week 3: (1+0.08) * week2
Week 4: (1+0.08) * week3

We can see that each succesive week we multiply by 1.08.
Week 1: 1*2 miles
Week 2: (1+0.08) * week1
Week 3: (1+0.08) * (1+0.08)* week1
Week 4: (1+0.08) * (1+0.08)* (1+0.08)* week1

If we use n for a number of week we can see that factor (1+0.08) appears n-1 times. We multiply this factor so we need to put n-1 in an exponent.
Our function is given by:

`d=2*1.08^(n-1) miles`
where n is number of a week