Question

state the practical meaning of the slope and y-intercept for the situation described.
the population, in millions, of a city t years after 1990 is given by ( p(t) = 3.1 + 0.07t ).
a. 3.1 million is the population of the city in 1991 and 3.17 million is the population in 1992.
b. 3.1 million is the population of the city in 1990 and 0.07 million is the decrease per year in the population.
c. 3.1 million is the population of the city in 1990 and 0.07 million is the increase per year in the population.
d. 0.07 million is the population of the city in 1990 and 3.1 million is the increase per year in the population.
please select the best answer from the choices provided
a
b
c

Explanation:

The function is in the form \( P(t)=b + mt \), where \( b \) is the y - intercept and \( m \) is the slope. For \( P(t)=3.1 + 0.07t \), when \( t = 0 \) (which corresponds to the year 1990, since \( t \) is years after 1990), \( P(0)=3.1 \), so 3.1 million is the population in 1990. The slope \( m = 0.07 \) represents the rate of change of the population per year. Since the slope is positive, it is an increase of 0.07 million per year. Option a is incorrect as it misinterprets the meaning of the values (it is not about 1991 and 1992 population in this context of slope and y - intercept interpretation). Option b is incorrect because the slope is an increase, not a decrease. Option d is incorrect as it swaps the meanings of the y - intercept and the slope.

Answer:

c. 3.1 million is the population of the city in 1990 and 0.07 million is the increase per year in the population.