15. Which of the following situations could be modeled by an exponential function? An 8 pound puppy gains 1.5 pounds per month for \( x \) number of months. The cost of an electrician that charges \( \$ 25 \) an hour for \( x \) number of hours. The amount in a savings account after \( \$ 75 \) is invested at a rate of \( 11 \% \) for \( x \) number of years. Theled by a car driving at 65 miles per hour for \( x \) number of hours. (1)
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The situation involving the savings account is a classic example of exponential growth. When money is invested at a certain interest rate, it doesn't just gain interest based on the initial amount; it also earns interest on the interest that has already been accumulated. This compound effect reflects the nature of exponential functions, showcasing how money can grow significantly over time, especially with a higher interest rate like 11%. On the other hand, the puppy's weight gain is modeled by a linear function, as it simply adds a fixed amount (1.5 pounds) each month. Similarly, the electrician's charge is linear too, operating on a steady hourly rate. These straightforward scenarios reflect how certain real-world situations can be effectively captured by linear models, contrasting with the more explosive growth seen with exponential functions. Choose wisely!
