1. The problem is to find the common ratio (base) of an exponential function that models the data points for money in an account: $144.07$, $374.53$, $605.68$, and $834.53$. 2. An exponential function has the form $$f(x) = a \cdot r^x$$ where $a$ is the initial amount and $r$ is the common ratio (multiplier). 3. To find $r$, we calculate the ratio between consecutive $y$ values: $$r_1 = \frac{374.53}{144.07} \approx 2.60$$ $$r_2 = \frac{605.68}{374.53} \approx 1.62$$ $$r_3 = \frac{834.53}{605.68} \approx 1.38$$ 4. Since the ratios are not exactly the same, the data is not perfectly exponential, but we can approximate $r$ by averaging these ratios: $$r \approx \frac{2.60 + 1.62 + 1.38}{3} = \frac{5.60}{3} \approx 1.87$$ 5. Therefore, the common ratio (base) of the exponential function that models the data is approximately $1.87$. 6. This means as $x$ increases by 1, the money in the account multiplies by about $1.87$ each time. Final answer: The common ratio/base is approximately $1.87$.