The number of pies available for sale at the Pie in the Sky Bakery varies over the
course of the day, and is given by P(t) = 30 - 212 +161, where t is the number of hours
since the store opens in the morning. What is the average rate at which this
number changes during the first t hours that the store is open?
It was probably p(t)=30-2t^2+16t
To find the average rate of change of the number of pies during the first t hours, we need to determine the change in the number of pies and divide it by the change in time.
The given equation P(t) = 30t - 212t + 161 describes the number of pies available for sale at the Pie in the Sky bakery at time t.
To find the change in the number of pies during the first t hours, we need to evaluate P(t) at t = t (number of hours since the store opens) and t = 0 (opening time). The delta symbol, Δ, represents the change in a value.
So, ΔP = P(t) - P(0) = (30t - 212t + 161) - (30(0) - 212(0) + 161)
= 30t - 212t + 161
Next, we need to find the change in time, which is t.
Therefore, the average rate of change of the number of pies during the first t hours is given by the ratio:
Average Rate of Change = ΔP / Δt
= (30t - 212t + 161) / t
= 30 - 212/t + 161/t
Thus, the average rate at which the number of pies changes during the first t hours that the store is open is described by the function 30 - 212/t + 161/t.