Micah works as a server at the local diner. He earns $50 per shift and $2.50 per table he serves. Micah's earnings can be represented by the function

Question

E(t)=50−2.5t


where E(t) represents his earnings per shift and t represents the number of tables he serves.

Part 1:

What does the 14 represent in the function: E(14)=50+2.5(14)

Responses

14 is the number of servers at the diner

14 is the amount of his tips during the shift

14 is the number of tables he served during his shift

14 is his earnings for the shift

Answer 1

In the function E(14) = 50 + 2.5(14), the 14 represents the number of tables he served during his shift. So the correct response is:

14 is the number of tables he served during his shift.

Answer 2

(The answer in part 2 was: E(14) = 85.)

Part 3:

What does your answer in Part 2 represent?

Responses

The number of people eating in the diner

The number of tables he served

His tips for the shift

His earnings for the shift

Answer 3

The answer in Part 2, E(14) = 85, represents his earnings for the shift. So the correct response is:

His earnings for the shift.

Answer 4

Jasmine evaluated a function.

Function: f(x) = 3 + √x+11
Step 1: f(60) = 3 + √60-11
Step 2: f(60) = 3 + √71
Step 3: f(60) = 3 + 8.42
Step 4: f(60) = 11.41

First, identify the step which was done wrong. Then, correctly evaluate the function.

Answer 5

Let's identify the incorrect step in Jasmine's evaluation of the function f(x) = 3 + √(x + 11).

1. Function given: \( f(x) = 3 + \sqrt{x + 11} \)
2. Step 1: She correctly substitutes x with 60.
   • \( f(60) = 3 + \sqrt{60 + 11} \)
3. Step 2: She incorrectly computes this as \( 3 + \sqrt{60 - 11} \). The correct computation should be:
   • \( f(60) = 3 + \sqrt{60 + 11} = 3 + \sqrt{71} \)
4. Step 3: She evaluates \( \sqrt{71} \) but incorrectly states it as approximately 8.42. The correct value of \( \sqrt{71} \) is approximately 8.426.
5. Step 4: Using 8.42 instead of the more accurate value results in the wrong final answer. The correct calculation should be:
   • \( f(60) = 3 + 8.426 \approx 11.426 \)

Correct Evaluation:

1. Start with the correct function:
   • \( f(60) = 3 + \sqrt{60 + 11} \)
2. Calculate \( \sqrt{71} \):
   • \( \sqrt{71} \approx 8.426 \)
3. Then calculate:
   • \( f(60) \approx 3 + 8.426 = 11.426 \)

So, the corrected evaluation of the function \( f(60) \) is approximately 11.426.

Answer 6

Sorry, the first part was f(x) = 3 + √x-11.

Answer 7

Thank you for the clarification. Given the corrected function \( f(x) = 3 + \sqrt{x - 11} \), let's reevaluate the steps to identify the mistake and correctly compute \( f(60) \).

1. Function given: \( f(x) = 3 + \sqrt{x - 11} \)
2. Step 1: Substituting \( x \) with 60:
   • \( f(60) = 3 + \sqrt{60 - 11} \)
3. Step 2: Simplifying:
   • \( f(60) = 3 + \sqrt{49} \)
4. Step 3: Calculating \( \sqrt{49} \):
   • \( f(60) = 3 + 7 \) (since \( \sqrt{49} = 7 \))
5. Step 4: Final calculation:
   • \( f(60) = 3 + 7 = 10 \)

Identifying the Mistake:

• The mistake in Jasmine's evaluation was in the original function she used. She wrote \( f(x) = 3 + \sqrt{x + 11} \), which is not the correct form. It should have been \( f(x) = 3 + \sqrt{x - 11} \).

Correctly Evaluated Function:

• The correct evaluation of \( f(60) \) is 10.