In order to gain popularity amongst high school students, Starbucks is creating a special winter promotion on Starbucks. The function below represents the cost of a Starbucks as a function of time (measured in days after December 4th).
Piece wise function
c(t)=
5; 0<= t <= 5
5 + 1; 5 < t <= 15
25; 15 < t <= 27
a) What would be the best dates to buy a Starbucks?
b) calculate c(9) - c(5)
costs nothing for the first 6 days,t = 0 through 5 ?
c(t) = 5+1 ???
no t, does not makes ense
5 + t
(a) clearly during the first 5 days, when the cost is just 5.
c(9) = 5+9 = 14
c(5) = 5
so, ...
To determine the best dates to buy a Starbucks, we need to find the intervals of time when the cost is lowest. In this case, we have a piecewise function that represents the cost of a Starbucks as a function of time.
The function is divided into three intervals:
1. 0 <= t <= 5: The cost is constant at $5.
2. 5 < t <= 15: The cost increases by $1 after the first 5 days.
3. 15 < t <= 27: The cost remains constant at $25.
a) To find the best dates to buy a Starbucks, we look for the intervals where the cost is lowest. From the function:
- For the interval 0 <= t <= 5, the cost is constant at $5.
- For the interval 5 < t <= 15, the cost increases to $5 + $1 = $6 after the first 5 days.
- For the interval 15 < t <= 27, the cost remains constant at $25.
Therefore, the best dates to buy a Starbucks would be within the first 5 days when the cost is $5.
b) To calculate c(9) - c(5), we substitute the values of 9 and 5 into the function.
c(9) = 5 + 1 = 6
c(5) = 5
Substituting these values into the equation, we have:
c(9) - c(5) = 6 - 5 = 1
Therefore, c(9) - c(5) is equal to 1.