Subjects algebra

Exponential Growth 5F9D91

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1. **State the problem:** We are given a table of values representing the amount of money in a savings account over time and need to determine if the function is linear or exponential. 2. **Identify the type of function:** - A linear function changes by a constant amount (additive change). - An exponential function changes by a constant ratio (multiplicative change). 3. **Calculate the ratios between consecutive y-values:** $$\frac{213.86}{178.39} \approx 1.198\quad,\quad \frac{257.14}{213.86} \approx 1.203\quad,\quad \frac{307.95}{257.14} \approx 1.198$$ 4. **Interpretation:** The ratios are approximately equal, indicating a constant multiplier, which suggests an exponential function. 5. **Conclusion:** The common ratio (multiplier/base) of the exponential function is approximately $1.2$. Thus, the function is best modeled as exponential with base approximately $1.2$.