# Math

The initial amount of sugar in fermenting a batch of beer is 5.5 grams. Over time the sugar decreases at a rate of 0.1grams per day.

a.What is the amount of sugar that remains after 7 days? 23 days?
- I got: 5.5-0.1x= A
- 5.5-0.1(7)= 4.8
- 5.5-0.1(23)= 3.2

b. If A represents the amount of sugar, write an equation for the amount of sugar that remains after x days?
-I got: 5.5-0.1x= A

c. Verify your equation is correct by taking the two ordered pairs from part (a) and finding the equation of the line that contains them

e. Algebraically and graphically, find the time it will take for the amount of sugar to drop below 2.8grams

f. How long will it take for the sugar to be completely gone?

I got a and b but kind of got stuck on the rest, thanks for the help in advance

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1. c) if x=7 , A = 4.8 ---> (7,4.8)
if x = 23, A = 3.2 ---> (23, 2.3)

slope = (2.3 - 4.8)/(23-7)
= -.1

so A = -.1x + b
for one of the points, say (7 , 4.8)
4.8 = -.1(7) + b
b = 4.8 + .1(7) = 55

so A = -.1x + 55
your equation from b) has been verified.

e.
2.8 = -.1x + 55
.1x = 55 - 2.8 = 52.2
x = 522 days

f) you want A = 0
0 = -.1x + 55
.1x = 55
x = 55/.1 = 550 days

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posted by Reiny
2. Thanks!

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