Chapter 1, Problem 334RE

For the following problems, consider a restaurant owner who wants to sell T-shirts advertising his brand. He recalls that there is a fixed cost and variable cost, although he does not remember the values. He does know that the T-shirt printing company charges $440 for 20 shirts and $1000 for 100 shirts.

334. In reality, the overall population is most likely increasing or decreasing throughout each year. Let’s reformulate the model as

   $P\left(t\right)=82.5-67.5\cos \left[\left(\pi /6\right)t\right]+t$, where t is time in months ( t = 0 represents January 1) and P is population (in thousands). When is the first time the population reaches 200,000?