Question

Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth rate was around 190%. In 1983, about 1700 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2005?

Write the exponential model: P= Blank 1 (1+ Blank 2)t

Answer 1

If the trend had continued unchecked, approximately 11,943 people would have died from AIDS in 2005.

Step-by-step explanation:

To write the exponential model for the spread of the AIDS epidemic, we'll use the formula P = P₀(1 + r)^t, where P₀ is the initial population, r is the growth rate as a decimal, and t is the number of time periods.

Given that the growth rate is 190%, which is equivalent to 1.9 as a decimal, and there were 1700 deaths in 1983, we can set up the model as:

P = 1700(1 + 0.019)^t

To find the number of people who would have died in 2005, we need to calculate the value of P when t = 2005 - 1983 = 22:

P = 1700(1 + 0.019)^{22}

Using a calculator or a computer to perform the calculation, we find that:

P ≈ 1700(1.019)^{22} ≈ 1700(1.464)^{22} ≈ 1700(7.024) ≈ 11,943.2

Therefore, if the trend had continued unchecked, approximately 11,943 people would have died from AIDS in 2005.