# 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'll fun 10 feet. On each subsequent day he'll double the distance he ran the previous day. So he'll 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 his plan for very long, but D' Andre is determined to make it work for at least two weeks.

How far will D' Andre have to run on the 14th day? In nearest tenth of a mile. (1 mile= 5280 feet)

If he sticks to the plan how far will he have ran in those two weeks? to the nearest mile.

Is there an equation for that one?^ or do I just have to add them all up?

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1. To find how far he runs in feet, f, on the given day d, you use the exponential equation f=5*(2^d). In calculus there is the sum function Σ, but there is another way, watch this:

Adding d from 1 to 3:

5*2+
5*2*2+
5*2*2*2=
5*(2^1+2^2+2^3) or 70.
So the simplest equation for the total number of feet after d days is 5(2^d+2^(d-1)+2^(d-2)…2^1)

So your final answer is that he would have to run 16384 feet (~3.1 miles) on day 14, but if he does he will have run a total of 163830 feet, or 31 miles.

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2. Formula: an= 5(2^n)

Day 1: a1=5(2^1)=10
Day 2: a2=5(2^2)=20
Day 3: a3=5(2^3)=40
Day 14:a14=5(a^15)=81,920
He will run 81,920 feet = 15.5 miles