Determine the point of intersection of the graphs of the functions $f(x)=60+4^x$ and $g(x)=4^{x+2}$.
Antwoord 1 correct
Correct
Antwoord 2 optie
There is no point of intersection.
Antwoord 2 correct
Fout
Antwoord 3 optie
$(2,76)$
Antwoord 3 correct
Fout
Antwoord 4 optie
$(3,124)$
Antwoord 4 correct
Fout
Antwoord 1 optie
The correct answer is not among the other options.
Antwoord 1 feedback
Correct: $$\begin{align*}
60+4^x=4^{x+2} &\Leftrightarrow 60+4^x = 4^2\cdot 4^x\\
&\Leftrightarrow 60+4^x =16\cdot 4^x\\
&\Leftrightarrow 60 =15\cdot 4^x\\
&\Leftrightarrow 4 = 4^x\\
&\Leftrightarrow x = 1.
\end{align*}$$
$f(1)=64$. Hence, the point of intersection is $(1,64)$.
Go on.
60+4^x=4^{x+2} &\Leftrightarrow 60+4^x = 4^2\cdot 4^x\\
&\Leftrightarrow 60+4^x =16\cdot 4^x\\
&\Leftrightarrow 60 =15\cdot 4^x\\
&\Leftrightarrow 4 = 4^x\\
&\Leftrightarrow x = 1.
\end{align*}$$
$f(1)=64$. Hence, the point of intersection is $(1,64)$.
Go on.
Antwoord 2 feedback
Wrong: There is a point of intersection.
See Properties exponential functions and Feature exponential functions.
See Properties exponential functions and Feature exponential functions.
Antwoord 3 feedback
Wrong: $f(2)=76$, but $g(2)=256$.
See Properties exponential functions and Feature exponential functions.
See Properties exponential functions and Feature exponential functions.
Antwoord 4 feedback
Wrong: $f(3)=124$, but $g(3)=1024$.
See Properties exponential functions and Feature exponential functions.
See Properties exponential functions and Feature exponential functions.