Creating an Exponential Model

formulate and solve an exponential equation that models areal-worldsituation.

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 isP(1+r/n)^nt, wherePrepresents the initial, or principal, balance;rrepresents theinterest rate;trepresents the time in years; andnrepresents the number of times the interest is compounded per year.

Part A

Identify the values ofP,r, andnin the expression P(1+r/n)^ntbased on Emma's situation. Then substitute those values into the formula to get a simplified exponential expression in terms of time.

Replace the variablesa,b, andcto write the expression.

part b

Since the card has $0 minimum payments for the first4 yearsit 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 in4 years?

Type the correct response. Use numerals instead of words. Round your answer to the nearest dollar.

In4 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.

Use numerals instead of words. Round your answer to the nearest tenth.

It will take about_yearsfor 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(1.015)^12t

300(1.0125)^T

300(1.15)^T

300(1.15)^12T

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?

After4 years,Emma would owe approximately

545

480

435

525

for her original purchase of $300.

It would take around

2.5

2.9

2.7

3.1

years for her balance to increase from $300 to $450.

I need help with all of this since I am not really good at algebra, I will not completly copy any answers you give.