Question

8. The graph is of a function in the form p(t) = a • bt. What is the function? (2 points

9. Use this function to estimate the boa constrictor population in 2 years, 3 years, and 4 years. (6 points: 2 points for each year, including 1 point for showing your work and 1 point for the answer)

t: Time in years
P(t): Estimated snake population at time t
2

3

4

10. What pattern do you see in years 2, 3, and 4? How is the snake population changing every year? (2 points

11. How is the snake population changing every two years? (1 point

Making a Decision:
12. Do you think the snake population can continue to grow in this way forever? Why or why not? (2 points)​

Answer 1

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Answer:

  8. p(t) = 5(2^t)

  9. 20, 40, 80

  10. doubles every year

  11. multiplies by 4

  12. no, it will soon exceed available habitat

Step-by-step explanation:

8. From the graph, a = p(0) = 5, and b = p(1)/p(0) = 10/5 = 2.

The function is ...

  p(t) = 5(2^t)

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9. You can read the values from the graph: 2 years: 20; 3 years: 40; 4 years: 80.

If you insist on evaluating the function, you have ...

  p(2) = 5(2^2) = 5·4 = 20

  p(3) = 5(2^3) = 5·8 = 40

  p(4) = 5(2^4) = 5·16 = 80

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10. The population doubles each year.

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11. In 2 years, the population doubles twice, so is multiplied by 4.

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12. No. Exponential functions don't last long in the real world. Eventually, required resources run out. In 15 years, there would be 163,840 snakes; in 20 years, there would be 5.2 million snakes; in 40 years, there would be 5.5 trillion snakes, about 44 snakes for every acre of land on earth (including polar areas).