Question

D'Andre has decided that he needs to get more exercise, so he is building a running regimen for himself. He decides that, beginning on Sunday, he will run 10 feet. On each subsequent day, he will double the distance he ran the previous day. So we will run 20 feet on Monday, 40 feet on Tuesday and so on. His track coach (who also happens to be his math teacher) told D'Andre that he won't be able to keep to his plans for very long, but D'Andre is determined to make it work for at least two weeks.

Answer 1

I found that according to his plan, he will run about 81920 feet or 15.5 miles on the 14th day using this formula (conversion = feet/5280)

\[10*2^{(14-1)}\]

The only thing I have left to find is how far he will have to run total in those two weeks. Thanks!

Answer 2

so you cant oslve just that equation?

Answer 3

Do I just do \[(10\frac {2^{14}-1}{(2-1)})/5280\]
If I do that, I get about 31 miles

Answer 4

That is how far he runs just that day in the first part.

Answer 5

i got 15

Answer 6

For the second part?

Answer 7

If so, that won't work. He runs over 15 miles \(just\) on the 14th day. I thought that was it too but then I found that it wouldn't work. I used \[a\frac{r^n-1}{r-1}\] where a is 10 because that is the starting number and r=2. n would be 14 because that is the last day.

Answer 8

then divided that answer by 5280

Answer 9

what's the formula for the geometric series?

Answer 10

The one I used to get the 14th day?

Answer 11

\[10*2^{(n-1)}\]

Answer 12

oh that's the one already
sooo let's seee

yes, everything that you did looks right ? so which part are you not sure of?

Answer 13

\(a\frac{r^n-1}{r-1}\) just apply this formula to get the sum and convert it to the proper unit

Answer 14

I just wanted to check the second part hehe xD Thanks!