Question
Diseases tend to spread according to the exponential
growth model. In the early days of AIDS, the growth factor
(i.e. growth multiplier not growth rate) was around 1.8. In
1983, about 1900 people in the U.S. died of AIDS. If the
trend had continued unchecked, how many people would
have died from AIDS in 2004?
people
growth model. In the early days of AIDS, the growth factor
(i.e. growth multiplier not growth rate) was around 1.8. In
1983, about 1900 people in the U.S. died of AIDS. If the
trend had continued unchecked, how many people would
have died from AIDS in 2004?
people
Ask by Cummings Daniels. in the United States
Nov 12,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
If the trend had continued unchecked, approximately 261,485 people would have died from AIDS in 2004.
Solution
To calculate the number of people who would have died from AIDS in 2004 based on the exponential growth model, we can use the formula for exponential growth:
where:
-
is the number of individuals at time , -
is the initial number of individuals, -
is the growth factor (multiplier), -
is the number of time periods (years in this case).
Given:
-
(the number of deaths in 1983), -
(the growth factor), - The time period from 1983 to 2004 is
years.
Now we can plug these values into the formula:
First, we calculate
:
Now, we can calculate
:
Therefore, if the trend had continued unchecked, approximately 261,485 people would have died from AIDS in 2004.
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The Deep Dive
To calculate the number of deaths from AIDS in 2004, we can use the exponential growth formula:
where
is the initial number of deaths,
is the growth factor (1.8), and
is the number of years since the initial measurement (1983 to 2004 is 21 years).
Using the numbers:
Calculating
gives approximately 142293.58. Therefore:
So, approximately 270,377,022 people would have died from AIDS in 2004 had the growth trend continued unchecked.
(However, this number is unreasonably high due to the simplified model—real-world factors usually counter such rapid growth.)