given the expense function $e(q) = 5 + 4q$, which table correctly represents the relationship between the…
given the expense function $e(q) = 5 + 4q$, which table correctly represents the relationship between the quantity $q$ and the total expenses $e(q)$?
Answer
Explanation:
Step1: Identify the expense function
The given linear function is: $$E(q) = 5 + 4q$$
Step2: Calculate the expense for $q = 0$
Substitute $q = 0$ into the function: $$E(0) = 5 + 4(0) = 5$$
Step3: Calculate the expense for $q = 1$
Substitute $q = 1$ into the function: $$E(1) = 5 + 4(1) = 9$$
Step4: Calculate the expense for $q = 2$
Substitute $q = 2$ into the function: $$E(2) = 5 + 4(2) = 13$$
Step5: Match results with the provided tables
The calculated values are $(0, 5)$, $(1, 9)$, and $(2, 13)$. Comparing these to the images, the fourth table contains these exact values.
Answer:
The fourth table:
| Quantity $q$ | Expense $E(q)$ |
|---|---|
| 0 | 5 |
| 1 | 9 |
| 2 | 13 |