Thread: Exponential and Logarithmic models

Here is the question that I do not understand and I don't know which model I am going to use:

HIV/AIDS. In 2003, an estimated 1 million people had been infected with HIV in the united states. If the infection rate increases at an annual rate of 2.5% a year compounding continuously, how many Americans will be infected with the HIV virus by 2010?

Can you help please. thank you!

Originally Posted by Anemori

Here is the question that I do not understand and I don't know which model I am going to use:

HIV/AIDS. In 2003, an estimated 1 million people had been infected with HIV in the united states. If the infection rate increases at an annual rate of 2.5% a year compounding continuously, how many Americans will be infected with the HIV virus by 2010?

Can you help please. thank you!

"compounded continuously" (without harvesting) means you should use the Malthusian model

So let be the number of Americans infected at time , be the initial amount infected, and be the rate of infection written as a decimal, then you have



Can you finish up?

Originally Posted by Jhevon

"compounded continuously" (without harvesting) means you should use the Malthusian model

So let be the number of Americans infected at time , be the initial amount infected, and be the rate of infection written as a decimal, then you have



Can you finish up?

Let r = 2.5% = 0.025
Let t= 2003 - 2010
P(t) = ?




Is this right?

Originally Posted by Anemori

Let r = 2.5% = 0.025
Let t= 2003 - 2010
P(t) = ?




Is this right?

yes, but i'd round it off to a whole number since we're talking about people.