Determine whether the given function is a solution to the given differential equation.
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Equation: L= -0.5D+34.
The water level be 26 feet in 16 days.
<u>Step-by-step explanation:</u>
Let us consider the initial level (x=0) of the water is 34 feet. Then its coordinate point can be written as (0,34).
The water is receding at the rate 0.5 feet per day, which given us the information that 0.5 is the slope since it is the rate of change and it is decreasing so it is a negative slope.
⇒m= -0.5.
The line equation is y = mx+c. Let us rewrite as L= mD+c.
Where L is the level of water(y-axis) and D is the days(x-axis) and c is y-intercept.
⇒L= (-0.5)D+c.
To find y-intercept, substitute (0,34) (the known point from the graph) in the equation. Also, the point in y axis when x=0 is y-intercept.
34= (-0.5)(0)+c.
c=34.
∴L= (-0.5)D+34.
To find the days when the water achieves level as 26 feet:
26 = (-0.5)D+34.
26-34= (-0.5)D.
-8 = (-0.5)D.
D= .
D= 16.