Use an exponential model and a graphing calculator to...

Use an exponential model and a graphing calculator to estimate the answer in each problem.
Determine how much time is required for an investment to double in value if interest is earned at the rate of $6.25 \%$ compounded annually.

Key Concepts

Logarithms

Logarithms are mathematical tools used to solve equations where the unknown variable appears as an exponent, such as in exponential growth and doubling time problems. By taking the logarithm of both sides of an exponential equation, one can isolate and solve for the time or rate, making this concept crucial for solving compound interest problems.

Doubling Time

Doubling time refers to the period it takes for an investment or quantity growing at a specific rate to double in value. It is a useful metric in exponential growth scenarios and is often estimated using formulas or rules like the Rule of 70. This concept helps in assessing the effectiveness of an investment's rate of return.

Compound Interest

Compound interest is the process in which interest is earned on both the initial principal and the accumulated interest from previous periods. This concept explains how investments grow faster compared to simple interest, since each period's interest is calculated on an ever-increasing balance. It is a fundamental principle in finance and investment calculations.

Exponential Growth Model

Exponential growth models describe how a quantity increases over time by a constant rate. For investments, they are typically represented by the formula P(1 + r)^t, where P is the principal amount, r is the interest rate per period, and t is the number of periods. This concept is essential for understanding how investments grow when interest is compounded over time.

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