Question

Nobody has figured this out yet.
In recent years we have seen a drop in number of cases of deaths from heart disease in the United States. Both men and women have shown a decline in death rates due to heart disease, but not at same rates. Let n be the number of years since 1970. Let M(n) be the number of deaths per 100,000 men n years after 1970. Let F(n) be the number of deaths per 100,000 women. Both the men and women were in the same age bracket, between 55 and 64. In 1970, the death rate of men in the bracket was 987.2/100000 and 351.6/100000. Over the years the death rate for men has decreased by 3% per year and 2.39% for women. Write a difference equation for the death rate of men at year n+1.

Answer 1

this is a strange problem but here's what I think it's saying

in 1970, the death percentage of men from 55 to 64 is 987.2/100000 (this is the fractional amount of 55 to 64 yr old men who have died in 1970)

so M(0) = 987.2/100000 since n = 0 refers to the year 1970

Answer 2

Since it's decreasing by 3% per year, this means that

M(1) = (987.2/100000)*(1 - 0.03)

or

M(1) = (987.2/100000)*(0.97)

for n = 1 (the year 1971)

for n = 2 (the year 1972), we apply the same 3% reduction to get

M(2) = (987.2/100000)*(0.97)(0.97)

M(2) = (987.2/100000)*(0.97)^2

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In general, the rate for any n is

M(n) = (987.2/100000)*(0.97)^n

this is extending the pattern shown above

Answer 3

She wants the answer in a form which looks like this \[M_{n+1}\] = a differential equation
where would the n+1 come into play?

Answer 4

hmm let me think, I have to somehow incorporate it into a difference equation, not thinking

Answer 5

maybe they want something like

M(n+1) = M(n) - 3% of previous rate

not sure

Answer 6

oh maybe it's

M(n+1) = M(n) - 0.03*M(n-1)

Answer 7

where n starts at n = 1 and M(0) = 987.2/100000

Answer 8

but I could be way off

Answer 9

I dont know if this will help you at all but most of the problems that I have had looked like this:
\[X_{n+1} = 1.08X_{n}+22(0.7)^{n} , X_{0}=400\]

and when I solve it, it looks like this:
\[X_{n} = 457.894(1.08)^{n} -57.894(0.7)^{n}\]

Answer 10

no sry, I guess I just forgot a lot about difference equations because this doesn't look familiar to me

Answer 11

well thanks for trying.

Answer 12

np, wish I could have helped more