Question

Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.E. Common ratio; growth multiplier) was around 1.9. In 1983, about 1800 people in the U.S. Died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2006?

Answer 1

4640933300 people would have died from AIDS in 2006.

Explanation:

Let the equation that models the growth in mortality because of AIDS be,

`A_n=A_0(1+r)^n`

Where
`A_n` = Number of deaths after n years

`A_0` = Deaths in first year

(1 + r) = Growth factor

n = number of years

Now we substitute the values in the equation,

`A_0=1800`

(1 + r) = 1.9

n = Number of years = 2006 - 1983 = 23 years

`A_n=1800(1.9)^(23)`

= 1800(2578296.28)

= 4640933300

Therefore, with the same death rate 4640933300 people would have died from AIDS in 2006.