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an exponential equation that goes through (3,64) and (5,1024)

Guest Jan 21, 2015

Best Answer 

 #1
avatar+18833 
+10

an exponential equation that goes through (3,64) and (5,1024)

$$\small{\text{
Exponential equation is:
$\quad \boxed{y=y_0*a^x}$
}}\\
\small{\text{
$
(1): \quad 64 = y_0*a^3 \quad | \quad (3,64)
$
}}\\
\small{\text{
$
(2): \quad 1024 = y_0*a^5 \quad | \quad (5,1024)
$
}}\\\\
\begin{array}{lrcl}
\hline
\\
\dfrac{(2)}{(1)}: &\dfrac{1024}{64} &=& \dfrac{y_0a^5}{y_0a^3} \\\\
&\dfrac{1024}{64} &=& \dfrac{a^5}{a^3} \\ \\
&16 &=&a^{5-3} \\
&16 &=&a^{2} \quad | \quad \sqrt\\
&4 &=&a\\
&a &=&4
\end{array}
\begin{array}{lrcl}
\hline
\\
(1): & 64 &=& y_0*4^3 \\
& 64 &=& y_0*64 \\
& 1 &=& y_0\\
& y_0 &=& 1\\
\end{array}
$\quad \small{\text{The exponential equation is:
}}\boxed{y=1*4^x=4^x}$$$

$$\\
\small{\text{
Proof:
}}\\
\small{\text{
$
\quad y(3) = 4^3 = 64 \quad okay!
$
}}\\
\small{\text{
$
\quad y(5) = 5^3 = 1024 \quad okay!
$
}}$$

heureka  Jan 21, 2015
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1+0 Answers

 #1
avatar+18833 
+10
Best Answer

an exponential equation that goes through (3,64) and (5,1024)

$$\small{\text{
Exponential equation is:
$\quad \boxed{y=y_0*a^x}$
}}\\
\small{\text{
$
(1): \quad 64 = y_0*a^3 \quad | \quad (3,64)
$
}}\\
\small{\text{
$
(2): \quad 1024 = y_0*a^5 \quad | \quad (5,1024)
$
}}\\\\
\begin{array}{lrcl}
\hline
\\
\dfrac{(2)}{(1)}: &\dfrac{1024}{64} &=& \dfrac{y_0a^5}{y_0a^3} \\\\
&\dfrac{1024}{64} &=& \dfrac{a^5}{a^3} \\ \\
&16 &=&a^{5-3} \\
&16 &=&a^{2} \quad | \quad \sqrt\\
&4 &=&a\\
&a &=&4
\end{array}
\begin{array}{lrcl}
\hline
\\
(1): & 64 &=& y_0*4^3 \\
& 64 &=& y_0*64 \\
& 1 &=& y_0\\
& y_0 &=& 1\\
\end{array}
$\quad \small{\text{The exponential equation is:
}}\boxed{y=1*4^x=4^x}$$$

$$\\
\small{\text{
Proof:
}}\\
\small{\text{
$
\quad y(3) = 4^3 = 64 \quad okay!
$
}}\\
\small{\text{
$
\quad y(5) = 5^3 = 1024 \quad okay!
$
}}$$

heureka  Jan 21, 2015

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