8. Order the expressions from least to greatest. V31,0, (V24 + 2), V90

Mathematics

1 answer:

algol [13]2 years ago

5 0

Answer:

29/9, $\sqrt[3]{90}$ , $\sqrt{31}$ , ( $\sqrt{24}$ +2)

Step-by-step explanation:

Convert to decimal values and compare:

29/9 3.222222222

cube root 90 4.481404747

sqrt31 5.567764363

(sgrt24 + 2) 6.898979486

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LUCKY_DIMON [66]

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a)

so, if the population doubled in 5 years, that means t = 5. So say, if we use an amount for "i" or P in your case, to be 1, then after 5 years it'd be 2, and thus i = 1 and A = 2, let's find "r" or "k" in your equation.

$\bf \textit{Amount of Population Growth}\\\\
A=Ie^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &2\\
I=\textit{initial amount}\to &1\\
r=rate\\
t=\textit{elapsed time}\to &5\\
\end{cases}
\\\\\\
2=1\cdot e^{5r}\implies 2=e^{5r}\implies ln(2)=ln(e^{5r})\implies ln(2)=5r
\\\\\\
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\textit{how long to tripling?}\quad 
\begin{cases}
A=3\\
I=1
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$\bf 3=e^{\frac{ln(2)}{5}\cdot t}\implies ln(3)=ln\left( e^{\frac{ln(2)}{5}\cdot t} \right)\implies ln(3)=\cfrac{ln(2)}{5} t
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b)

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A=10000\\
t=3
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\\\\\\
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