The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year, so we estimate that the population was growing at a rate of about 20 million/year at that time. Let's assume that the carrying capacity for world population is 100 billion. (Let the population, P, be in billions and t represent years with t = 0 corresponding to 1990.)
(a) Estimate the relative growth rate in 1990. (Round your answer to five decimal places.)

To estimate the relative growth rate in 1990, we can use the following formula:

\[
\text{Relative Growth Rate (r)} = \frac{\text{Growth Rate}}{\text{Population}}
\]

### Given Data:
- Population in 1990 (\( P_0 \)): \( 5.3 \) billion
- Growth rate in 1990 (\( dP/dt \)): \( 20 \) million per year, which is equivalent to \( 0.02 \) billion per year (since 1 billion = 1000 million).

### Step-by-step Calculation:
1. **Substitute the values into the formula**:
   \[
   r = \frac{0.02}{5.3}
   \]

2. **Calculate the relative growth rate**:
   \[
   r \approx \frac{0.02}{5.3} \approx 0.00377
   \]

So, the estimated relative growth rate in 1990 is approximately:

\[
\boxed{0.00377}
\]

This means that the population was growing at a rate of about 0.377% per year in 1990.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the growth rate change if the birth rates increased to 45 million per year?
2. What is the formula for exponential population growth, and how can it be applied here?
3. How does the concept of carrying capacity affect population growth over time?
4. How can you determine the time it would take for the population to double using the relative growth rate?
5. What would happen to the relative growth rate if the population increased to 10 billion while maintaining the same growth rate?

**Tip**: To estimate population growth over time, you can use the exponential growth formula \( P(t) = P_0 e^{rt} \), where \( r \) is the relative growth rate.

The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year, so we estimate that the population was growing at a rate of about 20 million/year at that time. Let's assume that the carrying capacity for world population is 100 billion. (Let the population, P, be in billions and t represent years with t = 0 corresponding to 1990.) (a) Estimate the relative growth rate in 1990. (Round your answer to five decimal places.)

Learn how to estimate the relative growth rate of the world population in 1990 using key mathematical concepts like exponential growth and the relative growth rate formula. This problem assumes a carrying capacity of 100 billion and a population growth rate of 20 million/year. Suitable for Grades 11-12.

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