Hello all! I'm new here.
Anyways, over the holidays, my grade 11 Pre-Calc teacher gave us an assignment to help us practice for our upcoming exam. I have done many of the questions on the assignment with minimal issue, but I'm not very bright when it comes to math and thus I have been quite stuck by a couple of them. I really would like some assistance to make sure I get the correct answers, as this is basically the sheet I am using to study for our final exam.
I have attempted all three of these 'problem questions', but don't feel I've done a very good job on them. My understanding is shaky at best, and math and I aren't getting along too well this semester!
Here they are:
1. The number of cups of coffee sold weekly is periodic over the course of a year. The maximum weekly sales of 12,000 cups usually occur around the end of January (week 4). The minimum weekly sales of 2,000 cups usually occur at the end of July (week 30).
The weekly sales can be modeled by a sinusoidal function.
a) Write an equation to model the weekly sales of coffee.
b) Use your equation to predict the total projected sales for the second week of August.
2. The amount of caffeine in your bloodstream follows an exponential pattern over time. In adults, the half-life is about 5.5 hours. If a 250mL coffee has 106mg of caffeineÖ
a) How much caffeine is in a 400mL coffee?
b) Write an exponential half-life function for the amount of caffeine in an adultís blood stream Ďtí hours after drinking a 400mL coffee.
c) Some individuals canít sleep with a high level of caffeine in their system at bedtime. Assume your bedtime is 10pm and that you canít sleep if there is more than 60mg of caffeine in your system. If you ingest a 400mL coffee at 8am and a 250mL coffee at 4pm, will you be able to fall asleep at 10pm?
3. A business predicts that spending $25,000 on advertising would yield a maximum profit of $200,000, and that spending less than $5,000 would result in a loss.
Assuming a quadratic model, if an owner does not advertise at all, what is the expected loss?
Thank you in advance for any tips or walkthroughs. Once I see how a question is done, I catch on pretty well!
All help is appreciated.