Questions: You are studying the population dynamics of an algae species that recently invaded a lake. You measured the amount of algae in the lake at the time of the invasion and then for six years afterward (shown in green dots below). You also conducted experiments showing this lake can support an algae population density of 200 cells per mm^2, marked below as a dashed orange line labeled K. What would you estimate the algae population density will be in two more years (at year 8)? Use the triangular markers on the graph to help you answer. (Note: population density can be modeled in the same manner as population size.)

You are studying the population dynamics of an algae species that recently invaded a lake. You measured the amount of algae in the lake at the time of the invasion and then for six years afterward (shown in green dots below). You also conducted experiments showing this lake can support an algae population density of 200 cells per mm^2, marked below as a dashed orange line labeled K. What would you estimate the algae population density will be in two more years (at year 8)? Use the triangular markers on the graph to help you answer. (Note: population density can be modeled in the same manner as population size.)
Transcript text: You are studying the population dynamics of an algae species that recently invaded a lake. You measured the amount of algae in the lake at the time of the invasion and then for six years afterward (shown in green dots below). You also conducted experiments showing this lake can support an algae population density of 200 cells per $\mathrm{mm}^{2}$, marked below as a dashed orange line labeled $K$. What would you estimate the algae population density will be in two more years (at year 8)? Use the triangular markers on the graph to help you answer. (Note: population density can be modeled in the same manner as population size.)
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Solution

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Solution Steps

Step 1: Find the current year and population density

The green dots represent algae population density over time. The last green dot corresponds to year 6 and a population density slightly above 70 cells/mm².

Step 2: Determine the population density at year 8

The question asks for the estimated population density at year 8. The triangular markers indicate population densities at different time points. We can see a marker for a population density of approximately 70 at year 6. The next closest marker lies just above 100 and a bit below 150 near year 8. This triangular marker gives a value of 115.

Final Answer: 115

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