Question
Solve each problem.Recycling $\quad$ A cost-benefit function $C$ computes the cost in millions of dollars of implementing a city recycling project when $x$ percent of the citizens participate, where$$C(x)=\frac{1.2 x}{100-x}$$(a) Graph $C$ in the window $[0,100]$ by $[0,10] .$ Interpret the graph as $x$ approaches $100 .$(b) If $75 \%$ participation is expected, determine the cost for the city.(c) The city plans to spend $\$ 5$ million on this recycling project. Estimate graphically the percentage of participation that they are expecting.(d) Solve part (c) analytically.
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2 x}{100-x}$. This function represents the cost in millions of dollars of implementing a city recycling project when $x$ percent of the citizens participate. The domain of this function is all real numbers except $x=100$, because the denominator becomes zero at Show more…
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Recycling A cost-benefit function $C$ computes the cost in millions of dollars of implementing a city recycling project when $x$ percent of the citizens participate, where $$ C(x)=\frac{1.2 x}{100-x} $$ (a) Graph $C$ in the window $[0,100]$ by $[0,10]$. Interpret the graph as $x$ approaches 100 (b) If $75 \%$ participation is expected, determine the cost for the city. (c) The city plans to spend $\$ 5$ million on this recycling project. Estimate graphically the percentage of participation that they are expecting. (d) Solve part (c) analytically.
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A large city has initiated a new recycling effort, and wants to distribute recycling bins for use in separating various recyclable materials. City planners anticipate the cost of the program can be modeled by the function $C(p)=\frac{220 p}{100-p}$ where $C(p)$ represents the cost (in $\$ 10,000$ ) to distribute the bins to $p$ percent of the population. (a) Find the cost to distribute bins to $25 \%, 50 \%$ and $75 \%$ of the population, then comment on the results; (b) graph the function using an appropriate scale; and (c) use the direction/ approach notation to state what happens if the city attempts to give recycling bins to $100 \%$ of the population.
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