The current temperature in degrees Celsius, where x equals the number of hours after noon, is 2x+10. Interpreting this equation, what is the initial value?
A. 10°C
B. −10°C
C. 2°C
D. −2°C
B. −10°C
The initial value is the value of the function when x is 0. Plugging in x=0 into the equation 2x+10 gives us 2(0)+10 = 10. However, the equation provides the temperature in degrees Celsius, making -10°C the initial value.
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?
A. The rate of change is −250 ft./sec., and the initial value is 3,000 ft.
B. The rate of change is 3,000 ft./sec., and the initial value is 250 ft.
C. The rate of change is 3,000 ft./sec., and the initial value is −250 ft.
D. The rate of change is 250 ft./sec., and the initial value is 3,000 ft.
D. The rate of change is 250 ft./sec., and the initial value is 3,000 ft.
The rate of change in the falcon's elevation is given as -250 ft/sec, since it is descending. The initial value is the initial height, which is 3,000 feet.
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.
A. The initial value of 35 represents the monthly fee.
B. The initial value of 50 represents the one-time membership fee.
C. The initial value of 50 represents the monthly fee.
D. The initial value of 35 represents the one-time membership fee.
B. The initial value of 50 represents the one-time membership fee.
In this case, the initial value corresponds to the fixed one-time membership fee that Hector would have to pay regardless of the number of months. Therefore, the initial value of 50 represents the one-time membership fee.
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.
A. The initial value of 1,200 represents the monthly cost of your phone.
B. The initial value of 1,200 represents the value of your cell phone at the time you purchase it.
C. The initial value of 75 represents the monthly cost of your phone.
D. The initial value of 75 represents the value of your cell phone at the time you purchase it.
B. The initial value of 1,200 represents the value of your cell phone at the time you purchase it.
In this context, the initial value refers to the starting value of the cell phone when it was purchased. The initial value of 1,200 represents the value of the cell phone at the time you purchase it before any depreciation.
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.
A. The initial value of 1,350 represents the fixed cost.
B. The initial value of 2.83 represents the variable cost.
C. The initial value of 2.83 represents the fixed cost.
D. The initial value of 1,350 represents the variable cost.
A. The initial value of 1,350 represents the fixed cost.
In this case, the fixed cost is the cost that remains constant regardless of the number of umbrellas produced. The initial value of 1,350 represents the fixed cost that the factory must pay no matter how many umbrellas they produce.