Answer:
20 days
Explanation:
We can model this situation using the linear equation, whose general form is
f(x) = mx + b, where m is the slope and b is the y-intercept
f(x) = -5/8x + 25/2, where f(x) is the amount remaining in the vitamin bottle and x is the number of days
Explaining the formula:
- We know that the slope must be negative since each successive dose depletes the bottle
- A slope of -5/8 means that the amount in the bottle decreases by 5/8 tsp for 1 day that passes
- 25/2 is simply 12 1/2 (a mixed number) converted to an improper fraction
- 25/2 is the y-intercept because the bottle starts with 25/2 tsp and when no doses are given (i.e., x = 0), there are 25/2 tsp in the bottle
We essentially want to find the x value that will make f(x) = 0 since that is when the bottle will be empty:
0 = -5/8x + 25/2
-25/2 = -5/8x
20 = x
We can check by plugging in 20 for x and see whether we get 0:
0 = -5/8(20) + 25/2
0 = -25/2 + 25/2
0 = 0