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Sphinxa [80]
3 years ago
7

A shop owner wants to market a new vest. The vest distributor will charge a reduced price for one size of the owner’s choice. Th

e owner knows that the size selected should be the mode of the sizes the shop sells. In one typical day, the shop owner sold the following sizes of vests:
40, 41, 41, 44, 44, 37, 38, 42, 41, 39, 44, 39, 37, 44, 42

Find the mode of the sizes?

A: 44
B: 40.9
C: 42
D: 46

PLS HELP
Mathematics
1 answer:
AlladinOne [14]3 years ago
7 0
The answer is 44 because the definition of Mode is the number that appears the most. The correct answer is A
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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 
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A=\textit{accumulated amount}\to &2\\
I=\textit{initial amount}\to &1\\
r=rate\\
t=\textit{elapsed time}\to &5\\
\end{cases}
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2=1\cdot e^{5r}\implies 2=e^{5r}\implies ln(2)=ln(e^{5r})\implies ln(2)=5r
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\boxed{\cfrac{ln(2)}{5}=r}\qquad therefore\qquad \boxed{A=e^{\frac{ln(2)}{5}\cdot t}} \\\\\\
\textit{how long to tripling?}\quad 
\begin{cases}
A=3\\
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\end{cases}\implies 3=1\cdot e^{\frac{ln(2)}{5}\cdot t}

\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
\\\\\\
\cfrac{5ln(3)}{ln(2)}=t\implies 7.9\approx t

b)

A = 10,000, t = 3

\bf \begin{cases}
A=10000\\
t=3
\end{cases}\implies 10000=Ie^{\frac{ln(2)}{5}\cdot 3}\implies \cfrac{10000}{e^{\frac{3ln(2)}{5}}}=I
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