The answer is the first one, because when you expand it you get -1/4 × 1, which equals -1/4, and -1/4 × -2y, which equals 1/2y. These are the same terms in the given expression -(1/2 + 1/4). I hope this helps!
To answer this item, we let x be the number of sessions at which the two rates would be equal.
For gym A, the total would become,
50 + 4x
while that of B is
30 + 6x
Equating these two expressions,
50 + 4x = 30 + 6x
The value of x from the equation is 10.
The calculation of the integral will give us the answer.
Amount = Int (2000e^(-0,2t))dt
With t = 0 to t = 10
A = 2000.In(e^(-0,2t))dt
Making U = -0,2t
U = -0,2t
dU/dt = d(-0,2t)/dt
dU/dt = -0,2
dU = -0,2dt
dt = dU/-0,2
_______________
Then,
A = 2000.Int (e^U).dU/-0,2
A = -10.000.Int(e^U)dU
A = -10.000.e^U
A = -10.000.e^(-0,2t) | (0,10)
A = -10.000.(e^(-2)) - [ -10.000.e^(0)]
A = -10.000.e^(-2) + 10.000
A ~ 8,646 Gallons
The least number which can be rounded off to 45,000 is 44,500. While the largest is 45,499.
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