Question

1. An empty baby pool is filled at a constant rate of 6 gallons per minute. The baby pool will hold 33 gallons of water when full. The volume, V, of water in the baby pool is a function of t, the time in minutes.

Which is the best description for the domain of the function V?

HINT: When will the baby pool fill up with water? (it only holds 33 gallons)

1Points
A
all values between 0 and 5.5

B
all values 0 and greater

C
all values between 0 and 32

2. A frozen yogurt shop charges $4.00 for a bowl of yogurt and $0.25 for each topping.

If the total charge for yogurt is dependent on the base price of the bowl of yogurt plus the number of toppings added, what is the value of y at the y-intercept of the line representing this situation?
Use the equation y = 0.25x +4. What is the y-intercept?

A
$0.25

B
$3.75

C
$4.00

3. Ethan is a professional videographer. It costs him $900 each month to operate his videography studio. Ethan's monthly profit, P, can be found by the function P = 350x - 900, Where x is the number of videography packages he sells.

On the graph of this function, what does the x-intercept represent?

Hint: The x-intercept indicates P=0 (there is no profit).

What does this mean for Ethan's studio?

A
the monthly minimum number of videography packages Ethan must sell to pay for his studio

B
the price of each video that Ethan sells

C
the amount Ethan pays for this videography studio

Answer 1

Answer: 1. all values between 0 and 5.5

2. $0.25

3. the monthly minimum number of videography packages Ethan must sell to pay for his studio

Explanation:

1. The rate of filling the baby pool= 6 gallons per minute.

let x be the number of minutes to fill the pool.

The maximum capacity of pool =
`V=6x=33\ gallons`

`\\\Rightarrow\ x=5.5\ minutes`

Therefore, in 5.5 minutes the pool will be filled completely.

Therefore, domain of the function = all values between 0 and 5.5

2. Given equation:
`y=0.25x+4.`

We know that the for the y intercept, put x=0, we get

`y=0.25+0=0.25`

Hence, the y intercept is $0.25.

3. Given function:
`P=350x-900`

For x intercept , put P=0, we get

`0=350x-900\\\Rightarrow\ x=(900)/(350)`, which shows the monthly minimum number of videography packages Ethan must sell to pay for his studio.