Need help with this power/energy problem

[awais]

I was working on the following problem:

Determine the power output as a function of time from an energy storage device for a four hour discharge period when it is known that for this type of system the power is a linear function of time, (Power) = a₀ - bt, where a₀ = 1.1(10⁵) W, b is a constant and t is the time. The energy stored in the device at the star of this process is 8.1(10⁸) J. Using your result calculate the power delivered at 2.4 hours into the discharge process.

Solution:

What i did was integrate the power equation to come up with an energy equation since

energy is the integral of power w.r.t time. i got the following expression

Energy = Energy _{(at t=0)} – (bt²)/2

Now we are given that At t=0; Energy = 8.1 × 10⁸ J

t=1; Energy = 8.1 × 10⁸ – b/2
t=2; Energy = 8.1 × 10⁸ – 2b
t=3; Energy = 8.1 × 10⁸ – 9b/2
t=4; Energy = 8.1 × 10⁸ – 8b


At t=2.4; Energy =8.1 × 10⁸ – 5.76b/2


I don't know how to calculate 'b' here. Am i doing it right or should i change my approach?

 

[daon2]

Since b is unknown you will be given additional information. I am thinking that maybe the "4 hour discharge period" might tell you something such as the energy left at t=4 is zero, allowing yourself to solve for b. But you will need to clarify that with your teacher.

Also, your integral should be:

\(\displaystyle E(t) = E_{t=0}+a_0t - \dfrac{1}{2}bt^2\)