1. The rate at which a city's population is growing can be represented by the function et, where t is the number of years since an economic boom. a) Write the definite integral which would calculate the number of people that move to the city in the third year. b) Calculate the number of people that move to the city in the third year using the integral you wrote in part a. Show all integration and calculation steps. Round your final answer to the nearest person. 2. Find the area between f (x) = 2.5x - 10 and the x-axis on the interval [0,8]. Use the Desmos calculator from class to help you as needed. a) Find the x-intercept(s) of f(x). Show all algebra. b) Write the integral that calculates the area between f (x) = 2.5x 10 and the x-axis on the interval [0,8]. Make sure to include all correct symbols and bounds. c) What is the antiderivative of f (x) = 2.5x - 10? d) The area between f(x) and the x-axis on the interval [0,8] is sq. units. e) Write the integral that calculates the area between f (x) = 2.5x - 10 and the x-axis on the interval [10,20]. You do not need to solve this integral. Make sure to include all correct symbols and bounds.