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 2.2. 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 2005?
people
(Note: once diseases become widespread, they start to
behave more like logistic growth, but don’t worry about
that for the purpose of this exercise)

Question

UpStudy AI · Accepted Answer

To calculate the number of people who would have died from AIDS in 2005 based on the exponential growth model, we can use the formula for exponential growth:

$$
N(t) = N_0 \cdot r^t
$$

where:
- $$N(t)$$ is the population at time $$t$$,
- $$N_0$$ is the initial population (the number of deaths in 1983),
- $$r$$ is the growth factor (the growth multiplier),
- $$t$$ is the number of time periods (years in this case) since the initial population.

Given:
- $$N_0 = 1900$$ (deaths in 1983),
- $$r = 2.2$$,
- The time period from 1983 to 2005 is $$t = 2005 - 1983 = 22$$ years.

Now we can plug these values into the formula:

$$
N(22) = 1900 \cdot (2.2)^{22}
$$

First, we need to calculate $$ (2.2)^{22} $$:

$$
(2.2)^{22} \approx  4,194,304.00 \quad \text{(using a calculator)}
$$

Now, we can calculate $$N(22)$$:

$$
N(22) = 1900 \cdot 4,194,304 \approx 7,988,177,600
$$

Thus, if the trend had continued unchecked, approximately **7,988,178,000** people would have died from AIDS in 2005.

This number is unrealistically high, indicating the exponential growth model's limitations in real-world scenarios, especially for diseases that eventually face limitations in spread.
Using the exponential growth model, if the trend had continued unchecked, approximately 7,988,178,000 people would have died from AIDS in 2005.

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