You are given: i. Mætt = ßt², t≥0 ii. l = 1,000 iii. lx+10 = 400 Calculate 1,0003.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

Transcribed Image Text:You are given:
i. Mr+t = ßt², t≥0
ii. l = 1,000
iii. lx+10
Calculate 1,000ß.
= 400
Expert Solution

Step 1: How to solve
To calculate 1000β, we can use the information provided in the problem. We have three equations:
i.
ii.
iii.
Let's start by using equation ii:
This means that the total number of lives at age x is 1000. Now, let's use equation iii:
This means that the total number of lives at age x+10 is 400. We can use these values to calculate the probability of surviving from age x to age x+10, denoted as
Now, let's use equation i with t = 10:
We know that the force of mortality (μ) is related to the probability of dying (q) as follows:
Since
Now, we can use the value of
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