Chapter 1.2, Problem 36E

Demand: Smartphones (See Exercise 35.) Here is another model for worldwide demand for smartphones:

$q\left(p\right)=36,900\left({0.968}^p\right)$ million units sold annually $\left(100\le p\le 200\right)$, where p is the unit price in dollars.²⁸

a. Use the demand function to estimate, to the nearest million units, worldwide sales of smartphones if the price is $120.

b. Extrapolate the demand function to estimate, to the nearest million units, worldwide sales of smartphones if the price is $210.

c. Model the worldwide annual revenue from the sale of smartphones as a function of unit price, and use your model to estimate, to the nearest billion dollars, worldwide annual revenue when the price is set at $120.

[Hint: $\text{Revenue}=\text{Price×Quantity}=p\cdot q\left(p\right)$

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