Tema
Q:
? QUESTION
The number of bacteria in a culture decreases according to a continuous exponential decay model. The initial population in a study is 400 bacteria, and there are
140 bacteria left after 6 minutes.
(a) Let \( t \) be the time (in minutes) since the beginning of the study, and
let \( y \) be the number of bacteria at time \( t \).
Write a formula relating \( y \) to \( t \).
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
\( y=\square \)
Q:
Graph each function. Then identify the domain and range of the function.
\( \begin{array}{lll}\text { 10. } y=-4 x^{2} & \text { 12. } f(x)=3 x^{2} \\ \text { 13. } f(x)=\frac{2}{3} x^{2} & \text { 14. } y(x)=1.5 x^{2} & \text { 15. } y=-\frac{1}{3} x^{2}\end{array} \)
Q:
QUESTION 4
Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \)
Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s).
Q:
1. The population of a rural town can be modelled by the function
\( P(x)=3 x^{2}-102 x+25000 \), where \( x \) is the number of years sin
2000. According to the model, when will the population be lowest?
Q:
QUESTION 3
The equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \).
Write down the equation of the new function that is formed when \( f \) is transformed as follows:
\( \begin{array}{ll}3.1 & \text { Shift two units to the left } \\ 3.2 & \text { Shift } 3 \text { units up } \\ 3.3 & \text { Shift } 1 \text { unit right and } 2 \text { units down } \\ 3.4 & \text { The equation of the new hyperbola has new asymptotes at } x=-4 \text { and } y=-1\end{array} \)
Q:
4. The function \( y=-5^{x} \) is reflected in the \( x \)-axis, reflected in the \( y \)-axis, and translated 2
units vertically. Determine the transformation function.
\( \begin{array}{llll}\text { a) } y=-5^{-x+2} & \text { b) } y=5^{-x}-2 & \text { c) } y=5^{-x}+2 & \text { d) } y=5^{-x+2}\end{array} \)
Q:
The manager of a hardware store sells batteries for \( \$ 5 \) a package. She
wants to see how much money she will earn if she increases the price
in \( 10 \notin \) increments. A model of the price change is the revenue
function \( R(x)=-x^{2}+10 x+3000 \), where \( x \) is the number of
\( 10 \notin \) increments and \( R(x) \) is in dollars. Explain how to determine the
maximum revenue.
Q:
Follow the seven step strategy to graph the following rational function.
\( f(x)=\frac{-x}{x+5} \)
Q:
2) Marca la opción correcta en cada caso:
a) ¿Cuál es la imagen de \( f(x)=2 \cdot\left(\frac{1}{2}\right)^{x} ? \)
b) ¿Cuál es la asintota de \( f(x)=\left(\frac{2}{3}\right)^{x}+1 ? \)
c) ¿Cuál es la ordenada al origen de \( f(x)=\left(\frac{2}{3}\right)^{x}+1 \)
Q:
Graph the exponential function.
\[ f(x)=\frac{1}{4}(2)^{x} \]
Plot five points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.
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