Question

Bill has decided to eat a healthier diet by decreasing the amount of salt he eats. He has decided to allow himself 35,000 milligrams of sodium in the first week of a new diet. Each week he will decrease the amount of sodium by 10%. How much sodium will he consume in the first 9 weeks of his new diet?

Answer 1

This looks like a geometric series problem in the form
a + ar + ar^2 + ... + ar^9
What would a and r be in your particular problem?

Answer 2

a = intial amount
r = percent

Answer 3

We're gonna add up sodium he consumes each week. a= the amount he consumes in the first week. so, what does a = ?

Answer 4

a = 35,000

Answer 5

yes. now, r might be a little trickier, but not too much. r needs to be a decimal that will reduce our calories by 10% for each successive term. What decimal can we multiply 35000 by to reduce it 10%?

Answer 6

.01

Answer 7

.9 ...... if you want to reduce something by 10% (which has a decimal equivalent of 0.1), multiply it by 1 - 0.1=0.9 r = 0.9
n, for this example is 9

Answer 8

The formula for the sum of our series is\[a \frac{ 1-r^{n} }{ 1-r }\]
Just plug in our a, n and r, and you should get the answer.