# Thread: Exponential and Logarithmic models

1. ## 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!

2. 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 $\displaystyle P(t)$ be the number of Americans infected at time $\displaystyle t$, $\displaystyle P_0$ be the initial amount infected, and $\displaystyle r$ be the rate of infection written as a decimal, then you have

$\displaystyle P(t) = P_0e^{rt}$

Can you finish up?

3. Originally Posted by Jhevon
"compounded continuously" (without harvesting) means you should use the Malthusian model

So let $\displaystyle P(t)$ be the number of Americans infected at time $\displaystyle t$, $\displaystyle P_0$ be the initial amount infected, and $\displaystyle r$ be the rate of infection written as a decimal, then you have

$\displaystyle P(t) = P_0e^{rt}$

Can you finish up?

$\displaystyle Let P_0=1000000$
Let r = 2.5% = 0.025
Let t= 2003 - 2010
P(t) = ?

$\displaystyle P(t) = 1000000e^{0.025(7)}$
$\displaystyle P(t) = 1191246.217 people$

Is this right?

4. Originally Posted by Anemori
$\displaystyle Let P_0=1000000$
Let r = 2.5% = 0.025
Let t= 2003 - 2010
P(t) = ?

$\displaystyle P(t) = 1000000e^{0.025(7)}$
$\displaystyle P(t) = 1191246.217 people$

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