The coefficient 7,000 represents the initial amount of the loan before any payments are made.

Supplemental Knowledge

Exponential functions are a type of mathematical function where a constant base is raised to a variable exponent. They are commonly used to model situations where growth or decay happens at a constant percentage rate over time. The general form of an exponential function is \(A \cdot B^ { kt} \), where:

• \(A\) represents the initial amount or starting value.
• \(B\) is the base, representing the growth (if greater than 1) or decay (if between 0 and 1) factor.
• \(k\) is a constant that adjusts the rate of growth or decay.
• \(t\) represents time.
  In the expression given, 7,000(0.90)^12t, we can break it down as follows:
• The coefficient 7,000 represents the initial loan amount before any repayments have been made.
• The base 0.90 indicates that Sully's loan amount decreases by 10% each month (since 1 - 0.10 = 0.90).
• The exponent 12t suggests that this decrease happens monthly over t years (since there are 12 months in a year).

Concepts to Actions

Imagine taking out a loan for the purchase of your new car; initially owing $20,000. Each month you make payments that reduce your balance by an estimated percentage, covering both interest payments and principal repayment; for instance if this percentage drops by approximately 5% each month due to these payments and interest adjustments then an exponential decay function similar to Sully's can model this situation effectively.
For instance, if your initial loan was%20,000 and it decreases by about 5% each month, after one year (12 months), your remaining balance can be calculated using an exponential function like \(20,000 \cdot ( 0.95) ^ { 12} \). This helps you understand how much you will owe over time and plan your finances accordingly.

Understanding how loans work and how they decrease over time can be crucial for managing personal finances effectively. At UpStudy, we offer specialized tools like our Algebra calculator to help you grasp these concepts effortlessly. Dive into our comprehensive resources and live tutor question bank for personalized guidance on algebraic expressions and more.
Explore UpStudy today – where learning meets practical application!