Question

diseases tend to spread according to the exponential growth model and the early days of AIDS in the growth factor was around 1.9 in 1983 about 1,500 people in the US died of AIDS if this trend had continued unchecked how many people would have died from Aids in 2005

Answer 1

Given the exponential model:

$f(x)=A\cdot b^x^{}$

Where A is the initial condition, b is the growth factor and x is a time-like variable.

We know that the growth factor is 1.9 and that 1500 people died of AIDS in 1983. If we make x to be the years passed since 1983, then 1500 is our initial condition (because 0 years passed). In our model:

$f(x)=1500\cdot1.9^x$

For 2005, x = 22:

$f(22)=1500\cdot1.9^{22}=2035497063$