College Algebra Question of the Day

1. $A(t)=P(2.05)^t$ for all $t$
2. $A(t)=2P(1.05)^t$ for all $t$ (correct answer)
3. $A(t)=P(1.10)^t$ for all $t$
4. $A(t)=P(1.05)^{2t}$ for all $t$

Explanation: This question tests college algebra skills: understanding exponential growth and decay models. Exponential functions model situations where quantities grow or shrink at rates proportional to their current value, expressed as f(t) = a * b^t. In this context, the balance adjustment scenario illustrates real-world applications like scaling initial investments. The correct answer works because it multiplies the initial coefficient by 2 while keeping the base unchanged. A common distractor fails because it alters the base or exponent incorrectly. To help students: Encourage practice with different initial conditions and rates; use graphing to visualize exponential growth and decay. Highlight the importance of identifying key parameters like base and time.