In Exercise, recall that for varying quantities produced and sold over time period t, the...

In Exercise, recall that for varying quantities produced and sold over time period t, the revenue function is R(t) = p(t) · q(t).

Finance—Market Analysis (continuation of Exercise 1): Use the sales and price functions from Exercise 1 to complete the following.

(a) Write the revenue function R(t). Do not algebraically simplify the function.

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(b) Compute R(3) and R′(3) and interpret each.

Exercise 1

Finance—Market Analysis: The PlayPro Company has projected that the monthly sales of their Bluetooth headphones can be modeled by

where t represents the number of months since the headphones were initially sold and q(t) represents the number of units sold in hundreds. They also project that the retail price of the headphones can be modeled by

 p(t) = 220 − t2 0 ≤ t ≤ 5

where t represents the number of months since the headphones were initially sold and p(t) represents the retail price in dollars.

(a) Evaluate q(3) and q′(3) and interpret each.

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(b) Evaluate p(3) and p′(3) and interpret each.