[填空题]
The average gasoline price, P, in cents per gallon, in USA 2019 can be modellew :81dmav8 hhsd*wtje6r 2z1nj by the functior 6nwz je12jt*n
P(t)=acos($15^{\circ}$t+$90^{\circ}$)+b,0≤t≤365,where t is the elapsed time, in days, since New Year's Eve 2018.
Part of the graph of y=P(t) is shown below.
1.Write down the value of b.
The average price of gasoline on the 1414th of January, 2019 was 328 cents per gallon.
2.Show that the value of a is equal to 56.
3.Hence calculate:
(1)the average gasoline price on the 1414th of February, 2019 ; P ≈ cents per gallon
(2)the minimum and maximum average prices of gasoline in USA 2019.
The cycle of average gasoline prices repeats every T days.$P_{min}$ ≈ cents per gallon; $P_{max}$ ≈ cents per gallon
4.Determine the value of T.
