College Algebra Question of the Day

1. $t\approx 11.6$ years
2. $t\approx 23.1$ years (correct answer)
3. $t\approx 17.3$ years
4. $t\approx 5.78$ years

Explanation: This question tests solving exponential equations related to real-world contexts in college algebra. Exponential equations model scenarios where quantities grow or decay at a constant rate over time, using the formula P = P_0 * e^(rt) where P is the final amount, P_0 the initial amount, r the rate, and t the time. In the given scenario, a savings account starts with $2500 and grows at a rate of 0.03 per year, students are expected to solve for t when it reaches $5000 using the provided values. The correct answer correctly applies the exponential formula to determine the time t ≈ 23.1 years, demonstrating understanding of growth processes. A common distractor arises from misinterpreting the growth rate, such as using 0.06 instead of 0.03, which leads to incorrect results. To help students, emphasize the importance of accurately interpreting the exponential formula and understanding the context of the problem. Practice solving similar equations with varying rates and initial values to build confidence.