Math Problem Statement

My bank balance can be modeled by B(t) = 5,000 − 400t dollars, where t is time in days since I opened the account. The balance on my account is ---Select--- by $400 per day.

Solution

The balance on your account is decreasing by $400 per day.

Explanation:

  • The given function is B(t)=5000400tB(t) = 5000 - 400t, where B(t)B(t) is the balance, and tt is time in days.
  • The term 400t-400t indicates a decrease of $400 for every day, since the coefficient of tt is negative.

Would you like further details or have any questions?

Here are 5 related questions:

  1. What will your balance be after 10 days?
  2. How long will it take for your balance to reach $0?
  3. How would the function change if your balance decreased by $300 per day?
  4. What is your initial balance at t=0t = 0?
  5. How can you graph the function B(t)B(t) to visualize the change?

Tip: To find how fast something is changing, always look at the coefficient of the variable representing time!

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Rate of Change

Formulas

B(t) = 5000 - 400t

Theorems

Rate of change of a linear function

Suitable Grade Level

Grades 6-8