You are given mx kx for all x 0 and 10p35 081 Calculate 2

You are given m(x) = kx for all x > 0 and 10p35 = 0.81. Calculate 20|20q40.

Solution

Easiest approach is to calculate

_tp_x = e ^{(integral from 0 to t) µx+sds}

= e ^{(integral from 0 to t) k(x+s)ds}

= e ^kt(x+t/2) .

Now you can find k via t = 10, x = 35 and then substitue with t = 20, x = 40.

As ₁₀p₃₅ = 0.81, and ₁₀p₃₅ = e ^{k[35u+0.5u 2 ]} = e ^400k ,

Thus,

we have e ^400k = 0.81.

Similarly, we calculate ₂₀p₄₀ = e ^1000k = e ^{400k *(5/2)}

= (0.81) ^5/2

= 0.59049.