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 1600 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003?

Answer 1

To estimate the number of people who would have died from AIDS in 2003, assuming the exponential growth model with a growth factor of 1.9, we need to calculate the exponential growth from 1983 to 2003.

First, let's calculate the number of years between 1983 and 2003:
2003 - 1983 = 20 years

Using the exponential growth formula:

N = N0 * (growth factor)^t

Where:
N0 is the initial value (number of deaths in 1983)
(growth factor) is the common ratio or growth multiplier
t is the time in years

Given:
N0 = 1600 (number of deaths in 1983)
growth factor = 1.9 (common ratio)
t = 20 (years)

Using the formula, we can calculate:

N = 1600 * (1.9)^20

Calculating this expression:

N ≈ 1600 * 6.1917364224

N ≈ 9907.58

Therefore, if the trend had continued unchecked, approximately 9908 people would have died from AIDS in the U.S. in 2003.