Suppose the rate of change of the expected life span l at birth of people born in the United States can be modeled by where t is the number of years past 1920. Use integration and the data point for 2007, to find the function that models the life span. If it's necessary, round your calculations to three decimal places,

Question

Suppose the rate of change of the expected life span l at birth of people born in the United States can be modeled by  where t is the number of years past 1920. Use integration and the data point for 2007, to find the function that models the life span. If it's necessary, round your calculations to three decimal places, ​  ​

Quizplus · Accepted Answer

The rate of change of the life span can be represented as:

dL/dt = 11eb0d3b_9890_0967_9790_af0c67caf973_TB1243_11

We can integrate both sides to find the function that models the life span:

∫ dL = ∫ 11eb0d3b_9890_0967_9790_af0c67caf973_TB1243_11 dt
L = ∫ 11eb0d3b_9890_0967_9790_af0c67caf973_TB1243_11 dt
L = 11eb0d3b_9890_0967_9790_af0c67caf973_TB1243_01 + C

We can find the value of C using the data point for 2007, which is 87 years:

L(87) = 87
87 = 11eb0d3b_9890_0967_9790_af0c67caf973_TB1243_01 + C
C = 87 - 11eb0d3b_9890_0967_9790_af0c67caf973_TB1243_01

Substituting the value of C in the equation for L, we get:

L = 11eb0d3b_9890_0967_9790_af0c67caf973_TB1243_01 + (87 - 11eb0d3b_9890_0967_9790_af0c67caf973_TB1243_01)
L = 87

Therefore, the function that models the life span is L = 87.

Option B is the closest to 87, so it is the best choice.

Suppose the Rate of Change of the Expected Life Span