(a) Estimate the population of this group for the year 2030 . (b) What is the instantaneous rate of change of the population when \( \mathrm{t}=30 \) ? (c) Interpret your answer to part (b). (a) The population in 2030 will be \( \square \) million people.

To predict the population of a specific group for the year 2030, you need to know the current population and the growth rate. If we assume a certain growth rate (let's say 2% annually), simply apply that over the number of years leading up to 2030. For instance, if the current population is 5 million, by using the formula for future population growth, you would estimate the population to be roughly 6.3 million people in 2030, factoring exponential growth. For the instantaneous rate of change of the population at \( t = 30 \), utilize derivatives if you're working with a population growth function. If, for example, you have a model like \( P(t) = P_0 e^{kt} \), you would differentiate this to find \( P'(t) \). Plugging in \( t = 30 \), you'd be solving for the growth rate at that specific time, which could reveal that the population is increasing by, say, 0.8 million people per year at that point in time!