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

Question

UpStudy AI · Accepted Answer

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:

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

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

Given:
- $$N_0 = 1900$$ (the number of deaths in 1983),
- $$r = 1.8$$ (the growth factor),
- The time period from 1983 to 2004 is $$t = 2004 - 1983 = 21$$ years.

Now we can plug these values into the formula:

$$
N(21) = 1900 \cdot (1.8)^{21}
$$

First, we calculate $$ (1.8)^{21} $$:

$$
(1.8)^{21} \approx 137.63 \quad \text{(using a calculator)}
$$

Now, we can calculate $$N(21)$$:

$$
N(21) = 1900 \cdot 137.63 \approx 261,485
$$

Therefore, if the trend had continued unchecked, approximately **261,485 people** would have died from AIDS in 2004.
If the trend had continued unchecked, approximately 261,485 people would have died from AIDS in 2004.

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