Question

12. Diseases tend to spread exponentially. In the early days of AIDS, the growth rate was around 190%. In 1983, about 1700 people in the US died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 1990?people

Answer 1

The formula for exponential growth is given as

`\begin{gathered} f(x)=a(1+r)^x \\ \text{where } \\ a=initial\text{ amount } \\ r=\text{growth rate } \\ x=\text{ numer of years } \end{gathered}`

From the question, the given parameters are

`\begin{gathered} \text{ a=1700} \\ r=(190)/(100)=1.9 \\ x=1990-1983=7 \\ let\text{ number of people in that would have died in 1990 be y} \end{gathered}`

Then replace the parameters in the formula above

`\begin{gathered} y=1700(1+1.9)^7 \\ \\ y=1700(2.9)^7 \\ \text{then} \\ y=1700*1724.987 \\ y=2932479 \end{gathered}`

Hence

The number of people that would have died from Aids in 1990 will be 2932479