The current temperature in degrees Celsius, where x

Question

equals the number of hours after noon, is 2x+10
. Interpreting this equation, what is the initial value?

options:

−2°C
negative 2 degrees C

−10°C
negative 10 degrees C

10°C
10 degrees C

2°C

Answer 1

To interpret the equation \( T(x) = 2x + 10 \), where \( T(x) \) represents the temperature in degrees Celsius and \( x \) is the number of hours after noon, we want to find the initial value of the temperature.

The initial value corresponds to the temperature at the starting point of the time interval we're considering, specifically at \( x = 0 \) (which is noon).

Substituting \( x = 0 \) into the equation:

\[ T(0) = 2(0) + 10 = 0 + 10 = 10 \]

Thus, the initial temperature at noon is \( 10°C \).

Therefore, the correct answer is:

10°C

Answer 2

From a height of 3,000 feet, a falcon descends at a rate of 250 ft./sec. What is the rate of change in the falcon’s elevation, and what is the initial value?

options:

The rate of change is 3,000 ft./sec., and the initial value is −250
ft.
The rate of change is 3,000 ft./sec., and the initial value is negative 250 ft.

The rate of change is 250 ft./sec., and the initial value is 3,000 ft.
The rate of change is 250 ft./sec., and the initial value is 3,000 ft.

The rate of change is −250
ft./sec., and the initial value is 3,000 ft.
The rate of change is negative 250 ft./sec., and the initial value is 3,000 ft.

The rate of change is 3,000 ft./sec., and the initial value is 250 ft.

Answer 3

Let's analyze the situation based on the information provided:

• The falcon starts at a height (initial value) of 3,000 feet.
• The falcon is descending at a rate of 250 ft./sec.

The rate of change in elevation when descending is considered negative because the elevation is decreasing. Therefore, the rate of change of the falcon's elevation is:

\[ \text{Rate of change} = -250 \text{ ft./sec} \]

Now summarizing:

• Initial value: 3,000 feet (the height at which the falcon starts).
• Rate of change: -250 ft./sec (indicating a descent).

Based on this analysis, the correct answer is:

The rate of change is −250 ft./sec., and the initial value is 3,000 ft.

Answer 4

Hector would like to join a gym that has a one-time membership fee plus a monthly fee. He can use the function f(x)=35x+50
to model the cost of gym membership after x
months. Identify and interpret the initial value of the function.

options:

The initial value of 35 represents the monthly fee.
The initial value of 35 represents the monthly fee.

The initial value of 50 represents the monthly fee.
The initial value of 50 represents the monthly fee.

The initial value of 50 represents the one-time membership fee.
The initial value of 50 represents the one-time membership fee.

The initial value of 35 represents the one-time membership fee.

Answer 5

The function \( f(x) = 35x + 50 \) represents the total cost of gym membership after \( x \) months, where:

• \( 35x \) represents the monthly fee: \( 35 \) dollars per month (for each month \( x \)).
• \( 50 \) represents the one-time membership fee.

To identify the initial value of the function, we look at the cost when \( x = 0 \) (which means he has not yet spent any months in the gym):

\[ f(0) = 35(0) + 50 = 0 + 50 = 50 \]

Thus, the initial value \( f(0) = 50 \) represents the one-time membership fee.

Therefore, the correct interpretation is:

The initial value of 50 represents the one-time membership fee.

Answer 6

The function f(x)=−75x+1,200
represents the value of your cell phone x
months after you purchase it. Identify and interpret the initial value of the function.

options:

The initial value of 1,200 represents the monthly cost of your phone.
The initial value of 1,200 represents the monthly cost of your phone.

The initial value of 75 represents the monthly cost of your phone.
The initial value of 75 represents the monthly cost of your phone.

The initial value of 75 represents the value of your cell phone at the time you purchase it.
The initial value of 75 represents the value of your cell phone at the time you purchase it.

The initial value of 1,200 represents the value of your cell phone at the time you purchase it

Answer 7

The function \( f(x) = -75x + 1,200 \) models the value of your cell phone \( x \) months after you purchase it. In this function:

• The term \( -75x \) indicates that the value of the cell phone decreases by \( 75 \) dollars for each month \( x \) that passes.
• The constant term \( 1,200 \) represents the initial value of the cell phone at the time of purchase (when \( x = 0 \)).

To understand the initial value, we can evaluate \( f(0) \):

\[ f(0) = -75(0) + 1,200 = 0 + 1,200 = 1,200 \]

Thus, the initial value \( f(0) = 1,200 \) represents the value of the cell phone at the time you purchase it.

Therefore, the correct interpretation is:

The initial value of 1,200 represents the value of your cell phone at the time you purchase it.

Answer 8

A factory produces beach umbrellas. They have a fixed cost they must pay no matter how many umbrellas they produce, and a variable cost they must pay for each umbrella they produce. The cost of producing x
umbrellas is modeled by the function C(x)=2.83x+1,350
. Identify and interpret the initial value.

options:

The initial value of 1,350 represents the fixed cost.
The initial value of 1,350 represents the fixed cost.

The initial value of 1,350 represents the variable cost.
The initial value of 1,350 represents the variable cost.

The initial value of 2.83 represents the fixed cost.
The initial value of 2.83 represents the fixed cost.

The initial value of 2.83 represents the variable cost.

Answer 9

The function \( C(x) = 2.83x + 1,350 \) represents the total cost of producing \( x \) beach umbrellas. In this function:

• The term \( 2.83x \) represents the variable cost, which is the cost incurred for producing each umbrella (specifically, \( 2.83 \) dollars for each umbrella).
• The constant term \( 1,350 \) represents the fixed cost, which is the amount the factory must pay regardless of the number of umbrellas produced.

To identify the initial value, we evaluate the cost when no umbrellas are produced, that is, when \( x = 0 \):

\[ C(0) = 2.83(0) + 1,350 = 0 + 1,350 = 1,350 \]

Thus, the initial value \( C(0) = 1,350 \) represents the fixed cost of production.

Therefore, the correct interpretation is:

The initial value of 1,350 represents the fixed cost.