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Date Posted: 4 years ago
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(a) In 1998, t = 0.
P(0) = 0.4(0)^2 + 8.7(0) + 32 = 32
The population was 32,000 in 1998.
(b) In 2012, t = 2012 - 1998 = 14.
P(14) = 0.4(14)^2 + 8.7(14) + 32 = 232.2
The population will be 232,200 in 2012.
(c) For P(t) ≥ 500, 0.4t^2 + 8.7t + 32 ≥ 500
0.4t^2 + 8.7t - 468 ≥ 0
Solving the quadratic equation, we see that x ≤ -46.77 or x ≥ 25.02
This shows that the population will become 500 thousand in the year 25 years after 1998. This year is 1998 + 25 = 2023.
P(0) = 0.4(0)^2 + 8.7(0) + 32 = 32
The population was 32,000 in 1998.
(b) In 2012, t = 2012 - 1998 = 14.
P(14) = 0.4(14)^2 + 8.7(14) + 32 = 232.2
The population will be 232,200 in 2012.
(c) For P(t) ≥ 500, 0.4t^2 + 8.7t + 32 ≥ 500
0.4t^2 + 8.7t - 468 ≥ 0
Solving the quadratic equation, we see that x ≤ -46.77 or x ≥ 25.02
This shows that the population will become 500 thousand in the year 25 years after 1998. This year is 1998 + 25 = 2023.
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