Mathematical Models
A representation of a real-world situation using equations, graphs, or tables.
What is a mathematical model?
Define “fixed expense.”
What is an expense that stays the same each month (e.g., rent, insurance).
What is the simple interest formula?
What is I = P × r × t?
What is the simplified compound interest formula?
What is A = P(1 + r)^t?
Interpret slope from a graph showing savings over time.
What is Slope = savings rate (amount saved per month)?
In the equation y = 50x + 200, what does the slope and intercept represent?
What is rate of change (savings per month); and starting balance ($200).
Give three examples of variable expenses.
What are groceries, entertainment, and gas?
Find the interest for $500 at 4% for 3 years.
What is 500 × 0.04 × 3 = $60?
Find total for $1,000 at 5% for 2 years.
What is $1,102.50?
Which model best fits a constant rate of change?
What is a Linear model?
Write the linear equation for a line passing through (1, 3) and (4, 9).
What is y = 2x + 1?
You earn $3,000 per month. Rent is $900, car $400, food $300, and other bills $600. How much can you save if you save 20%?
What is $600 saved?
Find the total balance after 5 years if $1,000 earns 5% simple interest.
What is A = 1,250
Compare simple vs compound interest for $1,000 at 5% for 3 years.
What is Simple = $150; Compound ≈ $157.63
Apply budgeting and interest: $2,000 saved at 4% for 1 year — how much interest?
What is $80?
A car depreciates $1,500 per year from a $25,000 starting value. Write a linear model.
What is y =- 1,500x + 25,000?
Your monthly income is $2,800. Your expenses total $2,400. How much is left for savings?
What is $400 remaining?
Which variable doubles the interest faster — rate or time?
What is doubling either time or rate?
Explain how compound growth models exponential change.
What is interest earns interest?
You save $100 monthly starting with $200. Write the model.
What is y = 100x + 200?
A cell phone plan costs $40/month + $10 per GB of data. Write a cost model.
What is y = 10x + 40?
Explain how saving can be represented as a linear model.
What is total savings increases linearly over time; slope = monthly savings, intercept = initial savings?
Solve for rate if interest = $200, principal = $2,000, time = 2 years.
What is 200 = 2000 × r × 2 → r = 0.05 = 5%
Find the total for $2,000 at 3% for 5 years.
What is $2,318.55?
Compare a 5% 4-year loan vs a 4% 5-year loan of $1,000. Which is cheaper?
What is they are the same?