https://file.aiquickdraw.com/mathbot/file/1728605889748zhnaof2t.jpg

give me only the answers without the explanations

Here are the answers for the blanks in the image you provided:

1. \( P(t) = 2560 e^{kt} \)
2. \( P(10) = 2560 e^{10k} \)
3. \( k = \frac{1}{10} \ln \left(\frac{3040}{2560}\right) \approx 0.0169 \)
4. \( P(t) = 2560 e^{0.0169t} \)
5. \( P(44) = 2560 e^{0.0169 \cdot 44} \approx 5297 \, \text{million} \)
6. \( P(80) = 2560 e^{0.0169 \cdot 80} \approx 6824 \, \text{million} \)

Let me know if you'd like further clarification or have any other questions!

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Here are five related questions to expand your understanding:

1. How is the value of \( k \) calculated using logarithms?
2. What does the model \( P(t) = 2560 e^{0.0169t} \) tell us about population growth over time?
3. How would you use this model to predict the population in the year 2050?
4. Why is it important to assume that the growth rate is proportional to the population size?
5. Can you explain how \( P(44) \) and \( P(80) \) were calculated?

**Tip:** The exponential growth model \( P(t) = P_0 e^{kt} \) assumes that the growth rate remains constant over time, which is a simplification of real-world dynamics.

Use the fact that the world population was 2,560 million in 1950 and 3,040 million in 1960 to model the population of the world in the second half of the 20th century. Assume that the growth rate is proportional to the population size. What is the relative growth rate? Use the model to estimate the world population in 1994 and to predict the population in the year 2030.

Learn how to calculate the world population growth rate using an exponential model with given data points from 1950 and 1960. Find the relative growth rate and estimate the world population in 1994 and 2030. This problem involves concepts like exponential growth, natural logarithms, and is suitable for high school students in Grades 11-12.

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