A little help please?

[borinbuscadecuartos]

Hello i am having some trouble on this problem.

The retro virus HIV can be transmitted from mother to child during breast feeding. But under conditions of poverty or poor hygiene, the alternative to breastfeeding carries its own risk for infant mortality. These risks differ in that the risk of HIV transmission is the same regardless of the age of the child, whereas the risk of mortality due to artifical feeding is high for new borns but decreases with the age of the child. For this problem we will assume that the additional risk of death from artificial feeding is A= 5 x .785 raised by t and the additional risk from breastfeeding is B=2, where t is the child's age in months.

question a. at what is is the additional risk of HIV transmission from breast feeding the same as the additional risk from artificial feeding.
to solve this i did A=b, then i got 5 x .785 raised by 7 = 2, then i got 6.64 months which i would put as 7 months.

however i am having trouble with question b and c. for which age does breastfeeding carry smaller additional risk?
at birth, what is the additional risk for transmission for a child who is fed artifically? i am having trouble setting them up

 

[DrMike]

Hello i am having some trouble on this problem.

The retro virus HIV can be transmitted from mother to child during breast feeding. But under conditions of poverty or poor hygiene, the alternative to breastfeeding carries its own risk for infant mortality. These risks differ in that the risk of HIV transmission is the same regardless of the age of the child, whereas the risk of mortality due to artifical feeding is high for new borns but decreases with the age of the child. For this problem we will assume that the additional risk of death from artificial feeding is A= 5 x .785 raised by t and the additional risk from breastfeeding is B=2, where t is the child's age in months.

question a. at what is is the additional risk of HIV transmission from breast feeding the same as the additional risk from artificial feeding.
to solve this i did A=B, then i got 5 x .785 raised by 7 = 2, then i got 6.64 months which i would put as 7 months.

however i am having trouble with question b and c. for which age does breastfeeding carry smaller additional risk?
at birth, what is the additional risk for transmission for a child who is fed artifically? i am having trouble setting them up

If \(\displaystyle A=5\times 0.785^t\) and \(\displaystyle B=2\), it seems like the questions are :

a) For what t is A=B ?
b) For what t is A>B ?
c) When t=0, what is A-B ?

You've solved (a), you could solve (b) similarly :
\(\displaystyle 5\times 0.785^t > 2\) when \(\displaystyle 0.785^t > 0.4\), that is, when \(\displaystyle t\log0.785>\log0.4\), in other words, \(\displaystyle t<\frac{\log0.4}{\log0.785}\). I switched the inequality because I divided both sides by the negative number \(\displaystyle \log0.785\).

For (c) - if I've understood your questions correctly - just substitute t=0 into \(\displaystyle 5\times 0.785^t - 2\)... you should get \(\displaystyle 3\)

 

[barson90]

Please clarify the question.
You're saying A= 5 x .785

Which I'm assuming from your description means A = 5(0.785)^t
When you arbitrarily say "B=2" ... I can only guess that you mean A = 5(0.785)^t + 2 when breastfeeding.

Is this the case?