+0  
 
0
341
1
avatar

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

Guest Jan 21, 2015

Best Answer 

 #1
avatar+19620 
+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
 #1
avatar+19620 
+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

10 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.