At what rate is the area changing when t=30 minutes and t=65 minutes? Explain the meaning of each of your answers.
2007-08-15 22:11:45 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
A(t) = 600t - 6t²
A `(t) = 600 - 12t
A `(30) = 600 - 360 = 240 m² / min
A `(65) = 600 - 780 = - 180 m² / min
Expanding at a rate of 240 m² / min
Contracting at a rate of 180 m² / min
2007-08-19 22:49:58 · answer #1 · answered by Como 7 · 3⤊ 0⤋
A (t) = 600 (30)- 6 (900) = 18 000 - 5400 = 12,600 is the area at 30 minutes
A (t) = 600 ( 65 ) -6 (65)^2 = 39000 + 6 ( 4225 ) = 13,650
Between 30 and 60 minutes the rate of growth decreases.
when 600 -12 t = 0 or t =50 you should have the maximum because the 1st derivative of A(t) = 600t-6t^2 is
A'(t)= 600 - 12t = 0 t= 50
2007-08-22 21:44:30 · answer #2 · answered by Will 4 · 0⤊ 0⤋
Rate of change is the derivative of A(t) i.e.
d/dt[A(t)] = 600 - 12t
when t = 30, rate of change 600-360= 240
2007-08-16 05:38:26 · answer #3 · answered by unknown123 2 · 0⤊ 0⤋