1. Consider the graph below, and answer the following:

1. Set up the definite integral to calculate the area of the shaded region on the graph, where the red curve is the graph of the function

b. Find the area of the shaded region.
2. The velocity (in feet per second) of a moving object at various times t (in seconds) has been recorded and is modeled by the function , where the initial position is 0 feet.

a. Find the position function, s(t), where s is in feet.

1. Find the position of the object after 2 seconds.
2. Find the change in position of the object between 5 and 10 seconds.

3. Suppose that you are asked to write a program to model a city’s population growth. The growth rate of the city is given by the following function:

a. Choose three values of x between 5 and 20. 6, 8, and 10.

b. Find the function P(x) that models the population growth.

c. Complete the following table using the three values for x  chosen above by finding the population of the city for the given years.

e. If the population of this city follows this model in the future, interpret the meaning of the following integral: