Question

the life expectancy of american women ( t ) years after 1975 is given by ( a(t)=0.5 t + 78 ). complete parts (a) through (c) below.
(a) find and interpret the a - intercept of the graph of this function.
choose the correct interpretation of the a - intercept below.
a. the a - intercept is which means the life expectancy of american women was years in the year
b. the a - intercept is which means the life expectancy of american women was 0 years in the year

Explanation:

Step1: Find A-intercept (set t=0)

To find the A - intercept, we set \( t = 0 \) in the function \( A(t)=0.5t + 78 \). Substituting \( t = 0 \) into the function, we get \( A(0)=0.5\times0 + 78=78 \).

Step2: Interpret the A-intercept

Since \( t \) represents the number of years after 1975, when \( t = 0 \), it corresponds to the year 1975. The value of \( A(0) = 78 \) means that the life expectancy of American women was 78 years in the year 1975. So the correct interpretation is option A. The A - intercept is 78, which means the life expectancy of American women was 78 years in the year 1975.

Answer:

For the A - intercept calculation: \( A(0)=78 \). The correct option is A. The A - intercept is 78, which means the life expectancy of American women was 78 years in the year 1975. So filling in the blanks for option A: The A - intercept is \(\boldsymbol{78}\) which means the life expectancy of American women was \(\boldsymbol{78}\) years in the year \(\boldsymbol{1975}\). The correct option is A.