Question

the life expectancy of american women t years after 1975 is given by ( a(t)=0.5t + 78 ). complete parts (a) through (c) below
a. the a - intercept is 78 which means the life expectancy of american women was 78 years in the year 1975
the a - intercept is which means the life expectancy of american women was 0 years in the year
(b) what is the slope of the graph of this function?
the slope of the graph of this function is 0.5
(simplify your answer)
(c) interpret the slope as a rate of change
the rate of change of this function is
(simplify your answer)

Explanation:

Step1: Recall the slope-intercept form

The function is given in the form \( A(t) = mt + b \), where \( m \) is the slope and \( b \) is the y-intercept (A-intercept here). The slope \( m \) represents the rate of change.

Step2: Identify the slope from the function

Given \( A(t) = 0.5t + 78 \), comparing with \( A(t) = mt + b \), we see that \( m = 0.5 \).

Step3: Interpret the slope as rate of change

In the context of life expectancy \( A(t) \) (in years) and time \( t \) (years after 1975), the slope \( 0.5 \) means that for each additional year (increase in \( t \) by 1), the life expectancy \( A(t) \) increases by 0.5 years. So the rate of change is 0.5 years per year after 1975.

Answer:

0.5 years per year (or 0.5, representing an increase of 0.5 years in life expectancy for each year after 1975)