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
d. graph (don't worry about)
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
c. To verify the equation you obtained in part b, we can substitute the two ordered pairs from part a into the equation and see if it holds true.
For the first ordered pair (7, 4.8), we substitute x = 7 into the equation:
5.5 - 0.1(7) = 4.8
5.5 - 0.7 = 4.8
4.8 = 4.8
The equation holds true for the first ordered pair.
For the second ordered pair (23, 3.2), we substitute x = 23 into the equation:
5.5 - 0.1(23) = 3.2
5.5 - 2.3 = 3.2
3.2 = 3.2
The equation also holds true for the second ordered pair. Therefore, the equation 5.5 - 0.1x = A is correct.
e. To algebraically find the time it will take for the amount of sugar to drop below 2.8 grams, we can set up the equation:
5.5 - 0.1x = 2.8
Now, solve for x:
0.1x = 5.5 - 2.8
0.1x = 2.7
x = 2.7 / 0.1
x = 27
So, it will take 27 days for the amount of sugar to drop below 2.8 grams.
f. To find how long it will take for the sugar to be completely gone, we need to find the time when the amount of sugar remaining is 0 grams. We can set up the equation:
5.5 - 0.1x = 0
Solve for x:
0.1x = 5.5
x = 5.5 / 0.1
x = 55
So, it will take 55 days for the sugar to be completely gone.