Final answer:
Functions b and c describe exponential growth. Function b shows a painting's value tripling every twenty years, and function c shows a population's annual increase by 1.2%. Both functions exemplify the defining characteristic of exponential growth: quantity increasing by a consistent factor over equal time intervals. The correct answer is b. The value of a painting triples every twenty years and c. The population increases by 1.2% each year.
Step-by-step explanation:
To determine which functions describe exponential growth or decay, we should look for processes where the change is proportional to the current value. With exponential growth, we see the quantity increasing by a consistent factor over equal intervals of time. Conversely, exponential decay would show a quantity decreasing by a consistent factor over time. The function describing the strength of a beam being proportional to the square of its thickness does not represent exponential change—it represents a quadratic relationship.
However, the function describing the value of a painting tripling every twenty years does represent exponential growth, as the value increases by a consistent factor (triple) over equal time intervals. Similarly, a population increasing by 1.2% each year also exemplifies exponential growth because the population grows by a consistent percentage (thus, a consistent factor) each year. Lastly, the description of the height of water in a tank increasing by 0.1 inches per hour indicates linear growth, not exponential, as it increases by a constant amount rather than a constant factor. We can thus conclude that the functions b (the value of a painting tripling) and c (the population increasing by 1.2% each year) describe exponential growth. So, the correct answer is b. The value of a painting triples every twenty years and c. The population increases by 1.2% each year.