On a college campus of 20,000 students, a single student returned to campus infected by a disease. The spread of the disease through the student body is given by

y=

20,000

______________

1 + 19999e^-0.99t ( 20,000 is divided by the given number)

where y is the total number of infected students at time t (in days).

For the problems below, show all work. Include brief explanation for steps that are not obvious.

a) How many students are infected after 4 days?

b) The school will pivot to online teaching if 25% of the students are ill. What day will the campus return to online teaching? (Hint: what is 25% of 20,00

0? Where can you use that value in the model?)

c) Let's say that the college mandates that students social distance and wear masks. The spread of the disease is now modeled by

y=.

20,000

____________________ ( 20,000 is divided by the given number)

1 + 19999e^-0.4t

Repeat parts (a) and (b) with this new model.

OUESTION 2

The SMC club you're a member of wants to do a fundraiser for the Club Row event. You're in charge. A few members of the club will help you make the item you choose to sell for the fundraiser.Don't worry, they are good at following directions!

a) Pick something you and other members of the club could make. It could be cookies, brownies, coffee, etc. This will be something you make ahead of time and bring to campus. Explain with a few sentences what you picked and why you picked it.

b) Determine the cost of supplies. Explain where you got the numbers for the items. Use the questions below to guide your answer.

i) How much are the ingredients?

ii) Will you wrap up the item or put it in a container? How much is that?

iii) Any other cost considerations?

c) How much does it cost the club to make? Create a linear function to represent the Total Cost as a function of the number of items sold. To help you make the function, use the questions below. Explain with complete sentences and math work how you determined the cost. Total

Cost: C(x) = fixed cost + variable cost.

i) How much will it cost to make a batch of items (like cookies) ? How much will it cost to make a single item? This is your variable cost.

ii) Are there any fixed or one-time costs (like renting equipment)? If you have no fixed cost, assume a fixed cost of $100.

d) How much will you sell the item for? Use this price to create your revenue function:

R(x) =xp where p is your price. (Note: we can't create a price-demand equation without consumer data). Briefly explain how you decided on the price.

e) Compute the profit function P(x).

f) How many items do you need to sell in order to break-even? In other words, how many items will you need to sell for cost and revenue to be equal? Show all steps for your math.

g) Will you make a profit? What considerations need to be made to ensure a profit? Do you need to go back and adjust the price?