Questions: Find the average rate of change of a function The population of a certain town is growing at a constant rate. Suppose the population is 1200 initially, and after 5 years, the population is 1710. Express the rate at which the population is increasing? Provide your answer below: people per year

Solution Steps

To find the average rate of change of the population, we need to calculate the difference in population over the difference in time. This is done by subtracting the initial population from the final population and dividing by the number of years that have passed.

The initial population of the town is \( P_0 = 1200 \) and the final population after 5 years is \( P_f = 1710 \). The change in population over this period is calculated as: \[ \Delta P = P_f - P_0 = 1710 - 1200 = 510 \]

The time interval over which this change occurs is \( t = 5 \) years.

The average rate of change of the population per year is given by the formula: \[ \text{Rate of Change} = \frac{\Delta P}{t} = \frac{510}{5} = 102 \]

Final Answer