Everything must be typed, including math work in the space provided below each question.

Textbook:

\fb. Use calculus to find the green area by first finding a model (in Desmos) for each function (hint: the red curve is best modeled by a square root function y, wasqet (x)and the blue curve is best modeled by a simple quadratic function y, ~a(x?))Using Dasmos, determine an exponential model (of the form n{t) = ab) using exponential (with your given data set). Lett=0 correspond to September 1, 2024. Write that model below. Let nit) be the number of cases for time t, in days. Also, include a picture of your scatter plot and your function graphed on the same plane. In mathematics, we like to use base e because of its properties, included the fact that the exponential function with base e is its own derivative. Find an equivalent function using base e of the form n(t) = ae. Show work. Note: you will need to use the function you found in part b, and the goal is to replace the base b, with e\". g. Now, let's jump back to 2020 and say the rate of change of the corona virus {Covid 19) is given by the function f(t) = 10e?*%", where t is the number of days since September 1, 2020 and f is the total number of new cases. Find the definite integral of f from t=10 to 30. Interpret what that means. Show wark. Data for Part 1 September 1, 2024 230 October 1, 2024 737 October 23, 2024 1786 November 7, 2024 29993500 3000 2500 2000 1500 1000 500 0 Sep 3 Sep 18 Oct 3 Oct 18 Nov 2 Nov 17Title: Calculus, 11th Edition Subtitle: Larson Other CALCULUS Calculus , 11th Edition Ron Larson; Bruce H. Edwards ISBN-10: 1-337-27534-4 ISBN-13: 978-1-337-27534-7