Subjects algebra

Investment Interest

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1. The problem states that the function $f(x) = 1.69(1.03)^x$ models the value of an investment after $x$ years, where $1.69$ is the initial amount (in thousands) and $1.03$ is the growth factor per year. 2. The formula for exponential growth is $f(x) = P(1 + r)^x$, where $P$ is the initial principal, $r$ is the yearly interest rate (as a decimal), and $x$ is the number of years. 3. Comparing the given function $f(x) = 1.69(1.03)^x$ to the formula, we see that $1 + r = 1.03$. 4. To find the yearly interest rate $r$, subtract 1 from the growth factor: $$r = 1.03 - 1 = 0.03$$ 5. Convert $r$ to a percentage by multiplying by 100: $$0.03 \times 100 = 3\%$$ 6. Therefore, the yearly interest rate the investment is earning is 3%, which corresponds to option A.