P gives the population of a town t years after it was founded.What is the best interpretation for the following statement?The slope of the line tangent to the graph of P at t=2 is equal to −10 .Choose 1 answer:(A) After 2 years, the rate of change of the population decreased at a rate of 10 people per year per year.(B) After 2 years, the town's population decreased at a rate of 10 people per year.(C) Over the first two years, the town's population decreased by 10 people per year.(D) After 2 years, the town's population decreased at a rate of 10 people.
Q. P gives the population of a town t years after it was founded.What is the best interpretation for the following statement?The slope of the line tangent to the graph of P at t=2 is equal to −10 .Choose 1 answer:(A) After 2 years, the rate of change of the population decreased at a rate of 10 people per year per year.(B) After 2 years, the town's population decreased at a rate of 10 people per year.(C) Over the first two years, the town's population decreased by 10 people per year.(D) After 2 years, the town's population decreased at a rate of 10 people.
Population Rate of Change: The slope of the line tangent to the graph of P at any point represents the rate of change of the population at that specific time.
Slope at t=2: Since the slope at t=2 is −10, this means that at t=2, the population is decreasing at a rate of 10 people per year.
Interpretation of Slope: The correct interpretation of the slope being −10 at t=2 is that after 2 years, the town's population is decreasing at a rate of 10 people per year. This matches with choice (B).
More problems from Interpreting Linear Expressions