Question

Monthiy focial securty benefis ditter with the age a recipient decides to start receiving benefis. fecipionts whose monthy benefts are 51050 , if benefits start being De of 61, can have thei benefits inciease by 5130 per month for each year after 61 they delay starting their benefes. Note that the monthy bosefit does not increase if the a. Wrte the linear function that models the monhly benes y as a functan of age x at which benents are staned, for the starting ages from 61 to 70 . b. What monthly beneff would these recipients rechive it they started receiving benefits at age 70 ?

Answer 1

The linear function that models the monthly benefits is y = 130x + 51050. If recipients started receiving benefits at age 70, they would receive a monthly benefit of $60150.

Step-by-step explanation:

To write a linear function that models the monthly benefits as a function of the age at which benefits are started, we can use the formula y = mx + b, where y represents the monthly benefits and x represents the starting age. Given that the monthly benefits increase by $130 per month for each year after 61, we can determine that the slope, m, is 130. Since the monthly benefit does not increase if the starting age is less than or equal to 61, the y-intercept, b, is $51050. Therefore, the linear function that models the monthly benefits is y = 130x + 51050.

To calculate the monthly benefit that recipients would receive if they started receiving benefits at age 70, we substitute x = 70 into the linear function. Using the equation y = 130x + 51050, we have y = 130(70) + 51050 = 9100 + 51050 = $60150. Therefore, these recipients would receive a monthly benefit of $60150 if they started receiving benefits at age 70.

Learn more about Linear function modeling