Question

15. The fish population, in thousands, in a lake at time $t$, in years, is modelled by the following function: (p(t) = egin{cases} 3 + frac{1}{12}t^2, & ext{if } 0 le t le 6\ 2 + frac{1}{18}t^2, & ext{if } 6 < t le 12 end{cases}) This function describes a sudden change in the population at time $t = 6$, due to a chemical spill. a. Sketch the graph of $p(t)$. b. Evaluate $lim_{t o 6^-} p(t)$ and $lim_{t o 6^+} p(t)$. c. Determine how many fish were killed by the spill. d. At what time did the population recover to the level before the spill?

          15. The fish population, in thousands, in a lake at time $t$, in years, is modelled by the following function:
(p(t) = egin{cases} 3 + frac{1}{12}t^2, & 	ext{if } 0 le t le 6\ 2 + frac{1}{18}t^2, & 	ext{if } 6 < t le 12 end{cases})
This function describes a sudden change in the population at time $t = 6$, due to a chemical spill.
a. Sketch the graph of $p(t)$.
b. Evaluate $lim_{t	o 6^-} p(t)$ and $lim_{t	o 6^+} p(t)$.
c. Determine how many fish were killed by the spill.
d. At what time did the population recover to the level before the spill?

$15. The fish population, in thousands, in a lake at time t, in years, is modelled by the following function: (p(t) = egincases 3 + frac112t^2, extif 0 le t le 6 2 + frac118t^2, extif 6 < t le 12 endcases) This function describes a sudden change in the population at time t = 6, due to a chemical spill. a. Sketch the graph of p(t). b. Evaluate limt o 6^- p(t) and limt o 6^+ p(t). c. Determine how many fish were killed by the spill. d. At what time did the population recover to the level before the spill?$

Added by Rachel M.

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