QuestionA 600-gallon tank drains at 30 gallons/min. Find $W(t)=-30t+600$ .
(b) How much water is left after 3 min?
(c) Graph $W$ and identify intercepts. What is the t-intercept?

Studdy Solution

STEP 1

Assumptions1. The tank initially contains600 gallons of water. . The tank is being drained at a rate of30 gallons per minute.
3. The function $W(t)=-30 t+600$ represents the amount of water in the tank at time $t$ .

STEP 2

For part (b), we need to find the amount of water in the tank after minutes. We can do this by substituting $t=$ into the function $W(t)$ .
$W()=-30()+600$

STEP 3

Calculate the amount of water in the tank after3 minutes.
$W(3)=-30(3)+600=-90+600=510$ After3 minutes, the tank contains510 gallons of water.

STEP 4

For part (c), we need to graph the function $W(t)$ and identify the intercepts. The function $W(t)$ is a linear function with a negative slope of -30 and a y-intercept of600. This means the graph starts at (0,600) and decreases by30 for every increase in $t$ .

STEP 5

The x-intercept (or t-intercept) is the value of $t$ when $W(t)=0$ . We can find this by setting $W(t)=0$ and solving for $t$ .
$0=-30t+600$

STEP 6

olve the equation for $t$ .
$30t=600$ $t=600/30$ $t=20$ The t-intercept is (20,0), which means the tank will be empty after20 minutes.

STEP 7

The graph of the function $W(t)$ is a straight line that starts at (0,600) and intersects the x-axis at (20,0). The slope of the line is -30, which means the line is decreasing. The y-intercept is the initial amount of water in the tank (600 gallons), and the t-intercept is the time when the tank will be empty (20 minutes).

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QuestionA 600-gallon tank drains at 30 gallons/min. Find $W(t)=-30t+600$ .
(b) How much water is left after 3 min?
(c) Graph $W$ and identify intercepts. What is the t-intercept?

Studdy Solution

STEP 1

Assumptions1. The tank initially contains600 gallons of water. . The tank is being drained at a rate of30 gallons per minute.
3. The function $W(t)=-30 t+600$ represents the amount of water in the tank at time $t$ .

STEP 2

For part (b), we need to find the amount of water in the tank after minutes. We can do this by substituting $t=$ into the function $W(t)$ .
$W()=-30()+600$

STEP 3

Calculate the amount of water in the tank after3 minutes.
$W(3)=-30(3)+600=-90+600=510$ After3 minutes, the tank contains510 gallons of water.

STEP 4

For part (c), we need to graph the function $W(t)$ and identify the intercepts. The function $W(t)$ is a linear function with a negative slope of -30 and a y-intercept of600. This means the graph starts at (0,600) and decreases by30 for every increase in $t$ .

STEP 5

The x-intercept (or t-intercept) is the value of $t$ when $W(t)=0$ . We can find this by setting $W(t)=0$ and solving for $t$ .
$0=-30t+600$

STEP 6

olve the equation for $t$ .
$30t=600$ $t=600/30$ $t=20$ The t-intercept is (20,0), which means the tank will be empty after20 minutes.

STEP 7

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QuestionA 600-gallon tank drains at 30 gallons/min. Find W(t)=−30t+600W(t)=-30t+600W(t)=−30t+600. (b) How much water is left after 3 min? (c) Graph WWW and identify intercepts. What is the t-intercept?

Studdy Solution

STEP 1

Assumptions1. The tank initially contains600 gallons of water. . The tank is being drained at a rate of30 gallons per minute.3. The function W(t)=−30t+600W(t)=-30 t+600W(t)=−30t+600 represents the amount of water in the tank at time ttt.

STEP 2

For part (b), we need to find the amount of water in the tank after minutes. We can do this by substituting t=t=t= into the function W(t)W(t)W(t).W()=−30()+600W()=-30()+600W()=−30()+600

STEP 3

Calculate the amount of water in the tank after3 minutes.W(3)=−30(3)+600=−90+600=510W(3)=-30(3)+600=-90+600=510W(3)=−30(3)+600=−90+600=510After3 minutes, the tank contains510 gallons of water.

STEP 4

For part (c), we need to graph the function W(t)W(t)W(t) and identify the intercepts. The function W(t)W(t)W(t) is a linear function with a negative slope of -30 and a y-intercept of600. This means the graph starts at (0,600) and decreases by30 for every increase in ttt.

STEP 5

The x-intercept (or t-intercept) is the value of ttt when W(t)=0W(t)=0W(t)=0. We can find this by setting W(t)=0W(t)=0W(t)=0 and solving for ttt.0=−30t+6000=-30t+6000=−30t+600

STEP 6

olve the equation for ttt.30t=60030t=60030t=600t=600/30t=600/30t=600/30t=20t=20t=20The t-intercept is (20,0), which means the tank will be empty after20 minutes.

STEP 7

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QuestionA 600-gallon tank drains at 30 gallons/min. Find $W(t)=-30t+600$ .
(b) How much water is left after 3 min?
(c) Graph $W$ and identify intercepts. What is the t-intercept?

Assumptions1. The tank initially contains600 gallons of water. . The tank is being drained at a rate of30 gallons per minute.
3. The function $W(t)=-30 t+600$ represents the amount of water in the tank at time $t$ .

For part (b), we need to find the amount of water in the tank after minutes. We can do this by substituting $t=$ into the function $W(t)$ .
$W()=-30()+600$

Calculate the amount of water in the tank after3 minutes.
$W(3)=-30(3)+600=-90+600=510$ After3 minutes, the tank contains510 gallons of water.

For part (c), we need to graph the function $W(t)$ and identify the intercepts. The function $W(t)$ is a linear function with a negative slope of -30 and a y-intercept of600. This means the graph starts at (0,600) and decreases by30 for every increase in $t$ .

The x-intercept (or t-intercept) is the value of $t$ when $W(t)=0$ . We can find this by setting $W(t)=0$ and solving for $t$ .
$0=-30t+600$

olve the equation for $t$ .
$30t=600$ $t=600/30$ $t=20$ The t-intercept is (20,0), which means the tank will be empty after20 minutes.