Question

During your first week of training for a marathon, you run a total of 10 miles. You increase the distance you run each week by 20%. How many miles do you run during your twelfth week of training?

Answer 1

Would I use:\[a _{n}=a _{1}\times r ^{n-1}\]

Answer 2

and the common ratio is .2? because it's 20 PERCENT?

Answer 3

@iGreen

Answer 4

@phi

Answer 5

if you use 0.2 for r, the distance will get smaller for large n.
you want to use 1.2 for r

Answer 6

working on it

Answer 7

\[a _{n}=10\times 1.2^{n-1}\]

Answer 8

so that?

Answer 9

you know the first week is 10
you know the second week is 20% more or 0.2*10= 2 more , so 10+2= 12

Answer 10

20% of 10 is 2.0

Answer 11

so ad that every week

Answer 12

now test your equation, to make sure it "works"
at n=1 (first week) you get 10 Good!
at n=2 you get 10*1.2 = 12 also good.
I would say that is a good equation

Answer 13

how far you run is just your equation with n=12

Answer 14

its 32 miles

Answer 15

@qwertyboy56 the growth is exponential , so it will be larger than 32

Answer 16

so, it's\[a _{12}=10\times 1.2^{12-1}\]
\[a _{12}=10\times 1.2^{11}\]
\[=10\times 7.430083707\]
\[=74.30083707\]

Answer 17

right?

Answer 18

yes

Answer 19

i dont think its asking for a total

Answer 20

you run 74 miles on the 12 week
we could make a table (write down the distance each week, multiply by 1.2 to get the next week...) we will see it shoot up to 74 miles per week on the 12 week

Answer 21

Okay... Thank you so much! I just checked my answer in the back of the book... I just wanted to make sure I was doing it correctly, or I'd never learn XD