2 years ago

Who drove the fastest? Select the correct answer.

Mathematics

1 answer:

jolli1 [7]2 years ago

3 0

Answer:

Step-by-step explanation:

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$\bf P=1110.9e^{kt}\quad 
\begin{cases}
P=1200 &\textit{in thousands}\\
t=2 &\textit{in 2002}
\end{cases}\implies 1200=1110.9e^{k2}
\\\\\\
\cfrac{1200}{1110.9}=e^{2k}\implies ln\left( \frac{1200}{1110.9} \right)=ln(e^{2k})\implies ln\left( \frac{1200}{1110.9} \right)=2k
\\\\\\
\cfrac{ln\left( \frac{1200}{1110.9} \right)}{2}=k\implies 0.0385755\approx k\implies 0.0386\approx k\\\\
-------------------------------\\\\$

$\bf P=1110.9e^{0.0386t}\qquad 
\begin{cases}
t=14\\
\textit{year 2015}
\end{cases}\implies P=1110.9e^{0.0386\cdot 14}
\\\\\\
P\approx 1907.0747\implies about\ 1,907,075\textit{ once rounded up}$

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Step-by-step explanation:

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