Please show all work along with answers. Thanks!

Note that on Exercise 1, there is a typo in the form 100's birthday. It's simply just supposed to be grandfather's 100th birthday.

 

Exercise 1. Rosy is baking cupcakes for her grandfather's 100's birthday. She works 5 hours every day, and is able to make 4 cupcakes per hour on day 1. (a) If Rosy bakes two more cupcakes per hour each day, how many cupcakes would she have made by the end of day 4? (b) Express the total number of cakes Rosy baked in sigma notation Exercise 2. Using the graphs below calculate (a) (b) 10 10. (10 - x) dx 100-x dx (a) Graph of y = 10- x 10 Exercise 3. Given that f(x)g(x) dx = 8, (your answer will depend on r) 8 (b) Graph of y = 100-x2 S" (f(x)) dx = 12, and "(9(t)) dt = 3, find L [* (g(x) + rf(x)) dx. Exercise 4. A new brewery just opened and is starting to produce strawberry kombucha every day. The rate of production is 100 liters per day in the beginning, but declines as new flavors are introduced, and is completely phased out by day 10. The rate of production is given by the function L(t)=100 t2 liters per day, where t is time in days. Calculate the average amount of strawberry kombucha produced per day on the interval from t = 0 to t = 10 days. Hint: the result of Exercise 2 part (b) will be useful.