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Question Find the equation for water level LL receding at 0.5 ft/day when initial level is 34 ft. Determine how many days until level reaches 26 ft.

Studdy Solution

STEP 1

Assumptions1. The initial water level of the river is34 feet. . The water level is receding at a constant rate of0.5 foot per day.
3. We are asked to find the number of days it will take for the water level to reach26 feet.

STEP 2

We can model the water level of the river as a linear equation, where the slope represents the rate of change (receding rate) and the y-intercept represents the initial water level. The equation can be written as=Initial level−Receding ratetimesdays = Initial\, level - Receding\, rate \\times days

STEP 3

Now, plug in the given values for the initial level and receding rate to get the equation for the water level after d days.
=34−0.5d =34 -0.5d

STEP 4

To find out when the water level will be26 feet, we can set L equal to26 in our equation and solve for d.
26=34−0.d26 =34 -0.d

STEP 5

Rearrange the equation to isolate d on one side.
0.5d=34−260.5d =34 -26

STEP 6

Calculate the right side of the equation.
0.5d=80.5d =8

STEP 7

Finally, divide both sides of the equation by0.5 to solve for d.
d=/0.5d = /0.5

STEP 8

Calculate the number of days.
d=8/0.5=16d =8 /0.5 =16So, it will take16 days for the water level to reach26 feet.

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