Initially, one student had the flu.
The number of students who get the flu doubles every day.
Let time ($x$) be the number of days after day zero ($x=0$).
Complete the table for the number of students with the flu, $B$, on day $x$.
$x$
$0$
$1$
$2$
$3$
$4$
$5$
$6$
$7$
$B\left(x\right)$
Fill in the table with your values.
Find a model for $B\left(x\right)$ and enter it in Desmos above.$\qquad B\left(x\right)=$
Find the number of bacteria (in thousands) in the sample 4.5 hours after the initial time. Enter $x=4.5$ in Desmos and find the intersection. Give your answer to 3 decimal places.
Find $x$ when the number of bacteria in the sample reaches 100,000. Enter $y=100$ in Desmos and find the intersection. Give your answer to 3 decimal places.
Tranforming the graph of $f\left(x\right)=2^x$
Draw the graphs in Desmos above to help you.
The equation of the horizontal asymptote of $f\left(x\right)=2^x$ is .
The graph of $f\left(x\right)=2^x$ is
by
units to produce the graph of $g\left(x\right)=2^x+3$.
The equation of the horizontal asymptote of $g\left(x\right)=2^x+3$ is .
The graph of $f\left(x\right)=2^x$ is
to the
by
units to produce the graph of $h\left(x\right)=2^{x+4}$.
The equation of the horizontal asymptote of $h\left(x\right)=2^{x+4}$ is .
The graph of $f\left(x\right)=2^x$ is stretched
away from the
-axis with a scale factor of
to produce the graph of $p\left(x\right)=3\left(2\right)^x$.
The equation of the horizontal asymptote of $p\left(x\right)=3\left(2\right)^x$ is .
The graph of $f\left(x\right)=2^x$ is stretched
away from the
-axis with a scale factor of
to produce the graph of $q\left(x\right)=2^{\frac{1}{4}x}$.
The equation of the horizontal asymptote of $q\left(x\right)=2^{\frac{1}{4}x}$ is .
The graph of $f\left(x\right)=2^x$ is
in the
-axis to produce the graph of $r\left(x\right)=-2^x$.
The equation of the horizontal asymptote of $r\left(x\right)=-2^x$ is .
The graph of $f\left(x\right)=2^x$ is
in the
-axis to produce the graph of $r\left(x\right)=2^{-x}$.
The equation of the horizontal asymptote of $r\left(x\right)=2^{-x}$ is .
Graph the following functions on Desmos above.
$f\left(x\right)=2^x$
$g\left(x\right)=3^x$
$h\left(x\right)=5^x$
$j\left(x\right)=\left(\frac{1}{2}\right)^x$
$k\left(x\right)=\left(\frac{1}{3}\right)^x$
$l\left(x\right)=0.2^x$
For $f\left(x\right)=a^x$ where $a>0$, the equation of the horizontal asymptote is:
For $f\left(x\right)=a^x$ where $a>0$, the coordinates of the $y$-intercept are:
The domain of $f\left(x\right)=a^x$ where $a>0$ is $x\in$
.
The range of $f\left(x\right)=a^x$ where $a>0$ is $y\gt$
$, y\in$
.