Problem #1: Anna wants to have $17,000 in 8 years, by 2028. She will place some money into a savings account called "GORGIOUS" that pays 3.1% interest compounded monthly. Answer the following questions: (1) How much should Anna invest now to have $17,000 in 8 years? Solve the equation algebraically and round the answer to two decimals.

(2)Going to the bank, she meets her friend, Charla who was one of the best students in Math112 last year. Charla tells her that there is another investment, "SUPERIOR" that pays the same interest compounded continuously. Charla advises Anna to check which investment is better. How much money Anna will have in 8 years, by 2028, if she puts her money now - the same amount that you have determined in (1) - into the "SUPERIOR" savings account?

(3) Which investment is better, and why?

Problem #2: A city's population has been growing exponentially over the past several years. In 2010, the population was 220,000 people. In the year 2016, it was 290,000 people. You need to set up the exponential population growth function that models the exponential growth of the population as a function of the number of years since 2010, (Hint: Use the formula of the exponential growth model that is given in Example 2 on page 114 of the class notes, () = . ) Give a step-by-step solution answering the questions below.

(1) Display the points that you can determine reading the problem in a coordinate system below

(2) Plug in the values (coordinates of the two points) properly into the formula of the exponential growth model and solve for . Round the answer to 4 decimals.

(3) Using the formula of the exponential growth model with value that you determined in (2), evaluate the population in the year 2020.

(4) Graph the population growth function on your calculator and plot the function above.