Spocks Given assumptions of Tribble Growth: Initial Population = 1 3 days on space station No deaths while on board 10 offspring per breeding event 12 hours between generations All Individuals can have babies (Dr. Mccoy says, "They are born pregnant") Complete the following table for the number of tribbles at a given time. Time (hours) 0 12 24 36 48 Population 1 11 1. Graph the Points below. Decide on appropriate scales for the axes first. 2. Write out an exact exponential using the assumptions given above. Explain why the equation matches these assumptions. First, define what your input variable represents. Check your results using exponential regression on your calculator. 3. Was Spocks calculation correct? We're there 1,771,561 tribbles after 3 days?
Spocks Given assumptions of Tribble Growth:
- Initial Population = 1
- 3 days on space station
- No deaths while on board
- 10 offspring per breeding event
- 12 hours between generations
- All Individuals can have babies (Dr. Mccoy says, "They are born pregnant")
Complete the following table for the number of tribbles at a given time.
| Time (hours) | 0 | 12 | 24 | 36 | 48 |
| Population | 1 | 11 |
1. Graph the Points below. Decide on appropriate scales for the axes first.
2. Write out an exact exponential using the assumptions given above. Explain why the equation matches these assumptions. First, define what your input variable represents. Check your results using exponential regression on your calculator.
3. Was Spocks calculation correct? We're there 1,771,561 tribbles after 3 days?
4. What if the tribble population grew linearly? Use the points (0,1) and (12,11) to construct a linear equation for population growth.
5. Populations rarely grow at a linear rate. But they can also not grow exponentially forever, due to limited resources (food, water, space, etc). Spock mentions this as an assumption but does not use this in his calculation. What would the population curve look like if there were only enough resources for one million tribbles on the space station? Sketch the Curve below.
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