Creating an Exponential Model In this activity, you will formulate and solve an exponential equation that models a real- world situation. Emma doesn't have experience using credit cards. In fact, she just got her first one. She is also about to start her first year of college. She uses her new credit card to purchase textbooks for her classes. The total comes to $300. These are the terms of her credit card: - It has a 15% annual interest rate. The interest is compounded monthly. ' The card has $0 minimum payments for the first four years it is active. The expression that models this situation is P(1 + rm, where P represents the initial, or principal, balance; r represents the interest rate; t represents the time in years; and n represents the number of times the interest is compounded per year. Part A Identify the values of P, r, and n in the expression P(1 + )\" based on Emma's situation. Then substitute those values into the formula to write a simplified exponential expression in terms of time. Replace the variables r, n, and tto write the expression. Part B Since the card has $0 minimum payments for the first 4 years it is active, Emma wonders how much it will cost her if she doesn't pay off the $300 balance until after college. How much will she owe in 4 years? Type the correct response in the box. Use numerals instead of words. Round your answer to the nearest dollar. In 4 years, Emma will owe about $ Part C Emma also wonders how long it will take her balance of $300 to reach $450, assuming she doesn't make any payments toward it. Write the equation to represent the situation, and solve it using the inverse relationship between exponential and logarithmic expressions. Type the correct response in the box. Use numerals instead of words. Round your answer to the nearest tenth. It will take about years for Emma's balance to reach $450. Part D Emma notices that since her credit card balance compounds monthly, she is charged more than 15% of her initial loan amount in interest each year. She wants to know how much she would pay if the card were compounded annually at a rate of 15%. Which expression could Emma use to evaluate her balance with an annual compounding interest rate? 300(1.15)12t 3000.15)t 3000.015)12t 3000111253)i Part E How would the situation change if the interest on Emma's credit card were compounded annually rather than monthly, and she didn't make any payments toward the balance? Select the correct answer from each drop-down menu. After 4 years, Emma would owe approximately $ for her original purchase of $300. It would take around years for her balance to increase from $300 to $450