1.Create an interpretation of the following statement.
f(2)=150
A.After 2 hours, the travel magician will have made $150.
B.After 300 hours, the travel magician will make $2.
C.After 2 hours, the travel magician will make $300.
D.After 150 hours, the travel magician will have made $2.
2.What is the minimum and maximum group size if the minimum charge to a bus rental is $200, the maximum charge is $300, and the cost is determined by the function f(x)=5x+50? Give your answer as a statement and in function notation.
A.The statement f(30)=300 means that the group size of 30 reaches the minimum charge for the bus rental of $300, and f(50)=200 means that the group size of 50 reaches the maximum charge for the bus rental of $200.
B.The statement f(50)=200 means that the group size of 50 reaches the minimum charge for the bus rental of $200, and f(30)=300 means that the group size of 30 reaches the maximum charge for the bus rental of $300.
C.The statement f(50)=300 means that the group size of 50 reaches the minimum charge for the bus rental of $300, and f(30)=200 means that the group size of 30 reaches the maximum charge for the bus rental of $200.
D.The statement f(30)=200 means that the group size of 30 reaches the minimum charge for the bus rental of $200, and f(50)=300 means that the group size of 50 reaches the maximum charge for the bus rental of $300.
3.The soda shop's profit for a day is modeled with the function f(x)=50x+30 where x is the number of days. How much did the shop make after 6 days?
A.$330
B.$300
C.$230
D.$270
#1 A. Clearly 2 is what you know, and 150 is what you calculate
#2 D. Read each choice carefully. It's the only one which makes any sense in the context
#3. f(6) = 50*6 + 30 = 330
1. To interpret the statement f(2) = 150, we need to understand the function f(x). It means that when you plug the value 2 into the function f(x), the output is equal to 150.
Looking at the options:
A. After 2 hours, the travel magician will have made $150. This option aligns with the interpretation of f(2) = 150. The magician's earnings are represented by the function f(x), and after 2 hours, they will have made $150. This is the correct interpretation.
B. After 300 hours, the travel magician will make $2. This option doesn't align with the given interpretation. The input value is 2, not 300, and the output value is 150, not $2.
C. After 2 hours, the travel magician will make $300. This option doesn't align with the given interpretation. The output value is 150, not $300.
D. After 150 hours, the travel magician will have made $2. This option doesn't align with the given interpretation. The input value is 2, not 150, and the output value is 150, not $2.
Therefore, the correct interpretation is A. After 2 hours, the travel magician will have made $150.
2. To find the minimum and maximum group size for the bus rental, we need to analyze the function f(x) = 5x + 50 and the given minimum charge of $200 and maximum charge of $300.
Let's break down the function: f(x) = 5x + 50
The constant 50 represents a base charge, and the coefficient 5 represents the additional cost per person.
Based on the given information:
- The minimum charge for the bus rental is $200.
- The maximum charge for the bus rental is $300.
Let's find the values of x (group size) that correspond to these charges:
For the minimum charge of $200, we set f(x) = 200:
5x + 50 = 200
5x = 200 - 50
5x = 150
x = 150 / 5
x = 30
For the maximum charge of $300, we set f(x) = 300:
5x + 50 = 300
5x = 300 - 50
5x = 250
x = 250 / 5
x = 50
Now let's analyze the options:
A. The statement f(30) = 300 means that the group size of 30 reaches the minimum charge for the bus rental of $300, and f(50) = 200 means that the group size of 50 reaches the maximum charge for the bus rental of $200. This option doesn't align with the correct interpretation.
B. The statement f(50) = 200 means that the group size of 50 reaches the minimum charge for the bus rental of $200, and f(30) = 300 means that the group size of 30 reaches the maximum charge for the bus rental of $300. This option aligns with the correct interpretation.
C. The statement f(50) = 300 means that the group size of 50 reaches the minimum charge for the bus rental of $300, and f(30) = 200 means that the group size of 30 reaches the maximum charge for the bus rental of $200. This option doesn't align with the correct interpretation.
D. The statement f(30) = 200 means that the group size of 30 reaches the minimum charge for the bus rental of $200, and f(50) = 300 means that the group size of 50 reaches the maximum charge for the bus rental of $300. This option doesn't align with the correct interpretation.
Therefore, the correct interpretation is B. The statement f(50) = 200 means that the group size of 50 reaches the minimum charge for the bus rental of $200, and f(30) = 300 means that the group size of 30 reaches the maximum charge for the bus rental of $300.
3. To find how much the soda shop made after 6 days, we need to substitute x = 6 into the function f(x) = 50x + 30.
Let's calculate it:
f(6) = 50 * 6 + 30
f(6) = 300 + 30
f(6) = 330
Therefore, the soda shop made $330 after 6 days.
The correct answer is A. $330.