solve problems, using the derivative, that involve instantaneous rates of change, including problems arising from real-world applications (e.g., population growth, radioactive decay, temperature changes, hours of daylight, heights of tides), given the equation of a function* Sample problem: The size of a population of butterflies is given by the function where is the time in days. Determine the rate of growth in the population after 5 days using the derivative, and verify graphically using technology.