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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).
