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? (1 point)
Responses
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.
The rate of change is 3,000 ft./sec., and the initial value is 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 3,000 ft./sec., and the initial value is −250 ft.
The correct response is: The rate of change is -250 ft./sec., and the initial value is 3,000 ft.
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.(1 point)
Responses
The initial value of 35 represents the one-time membership fee.
The initial value of 35 represents the one-time membership 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 monthly fee.
The correct response is: 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.(1 point)
Responses
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.
The initial value of 1,200 represents the value of your cell phone at the time you purchase it.
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 1,200 represents the monthly cost of your phone.
The correct response is: The initial value of 1,200 represents the value of your cell phone at the time you purchase it.
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.(1 point)
Responses
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 variable cost.
The initial value of 2.83 represents the variable cost.
The initial value of 1,350 represents the fixed cost.
The initial value of 1,350 represents the fixed cost.
The initial value of 2.83 represents the fixed cost.
The correct response is: The initial value of 1,350 represents the fixed cost.
What was the result of the development of the Silk Road? Select the two correct answers.
(1 point)
Responses
It brought new ideas such as Buddhism into China.
It brought new ideas such as Buddhism into China.
It enabled the Shang to expand Chinese territory.
It enabled the Shang to expand Chinese territory.
It made travel easier between northern and southern China.
It made travel easier between northern and southern China.
It allowed the Chinese to learn the process of making silk.
It allowed the Chinese to learn the process of making silk.
It increased the prosperity of Han merchants.
It increased the prosperity of Han merchants.
It caused the geographic isolation of the Chinese dynasties.
The correct answers are:
- It brought new ideas such as Buddhism into China.
- It made travel easier between northern and southern China.
The rate of change in the falcon's elevation is -250 ft./sec. To determine this, we need to know that the negative sign indicates that the falcon is descending, as opposed to ascending. Therefore, the rate of change is -250 ft./sec.
The initial value is 3,000 ft. This is the starting point or the height before the falcon begins its descent. The initial value represents the initial condition of the scenario, which in this case is starting at a height of 3,000 ft.
So, the correct response is: The rate of change is -250 ft./sec., and the initial value is 3,000 ft.