1. Jasmine and Sarah want to design a website for the spring sale of a clothing store. The sale will start at 8 am and close at 8 pm on May 14. To build the website, they have to be able to predict the number of online customers that day. Each one has different predictions for the number of online customers that day.
a. Sarah believes that the number of online customers will start at a minimum of 2 thousand online customers at 8 am and then it will increase to a maximum of 12 thousand customers at 2 pm. Let S(tJ) be the sinusoidal function which gives the amount of online customers on the website (in thousands) / hours after 8 am on May 14 according to Sarah's predictions.
Write a formula for the function S(t) for 0≤t≤12.
S(t)=
b. On the other hand, Jasmine believes that there will be 3 thousand online customers at 8 am and that the number of online customers will reach a maximum of 10 thousand at 2 pm. Let (r) be the quadratic function which gives the amount of online customers on the website (in thousands) 1 hours after 8 am on May 14 according to Jasmine's predictions.
Write a formula for J(t) for 0≤t≤12.
c. How many online customers does Sarah's model predict there will be at 7 pm on May 142
d. How many online customers does Jasmine's model predict there will be at 7 pm on May 14?
e. At what time(s) is the difference in predicted online customers between the two models the greatest? What is the discrepancy? Solve by graphing with your calculator or using Desmos.
f. At what times, if any, do the two models predict the same number of online customers? Solve by graphing with your calculator or using Desmos
