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 mea s 78 years in the year 1975
b. the a - intercept is which mean years per life expectancy 0 years in the year
(b) what is the slope of the graph of this years of age per year after 1975.
the slope of the graph of this function is life expectancy per year.
(simplify your answer)
years after 1975 per years of age
(c) interpret the slope as a rate of change
the rate of change of this function is
(simplify your answer)

Explanation:

Part (b)

Step1: Recall 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).

Step2: Identify slope from the function

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

Step1: Understand rate of change for linear function

For a linear function \( y = mx + b \), the slope \( m \) represents the rate of change of \( y \) with respect to \( x \). Here, \( A(t) \) is life expectancy and \( t \) is years after 1975.

Step2: Interpret the slope as rate of change

The slope is \( 0.5 \), so the rate of change of life expectancy (\( A(t) \)) with respect to years after 1975 (\( t \)) is \( 0.5 \) years of life expectancy per year.

Answer:

\( 0.5 \)

Part (c)