## Related questions with answers

A traffic engineer determines that the number of cars passing through a certain intersection each week can be modeled by $C(x)=0.02x^3+0.4x^2+0.2x+35$, where x Is the number of weeks since the survey began. A new road has just opened that affects the traffic at that intersection. Let $N(x)=C(x)+200$.

Emergency roadwork temporarily closes off most of the traffic to this intersection. Write a function R(x) that could model the effect on C(x) Explain how the graph of C(x) might be transformed into R{x).

Solution

VerifiedIt says that most of the traffic is closed, so one possibility would be that the traffic reduced to $10\%$ of the traffic modeled by $C(x)$. In that case:

$R(x)=0.1C(x)=\color{#19804f}0.002x^3+0.04x^2+0.02x+3.5$

This transformation is $\textit{vertical compression}$ of $C(x)$.

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