Tema
Q:
13. A farmer has 450 m of fencing to enclose a rectangular area and divide it into
ri two sections as shown.
a) Write an equation to express the total area enclosed as a function of the
width. \( 2 x+2 y=450 \)
b) Determine the domain and range of this area function.
c) Determine the dimensions that give the maximum area.
Q:
The percent of women in a country's civilian labor force can be modeled fairly well by the function
\( f(x)=\frac{68.24}{1+1.085 e^{-x / 24.77}} \), where x represents the number of years since 1950. Answer parts a and \( b \).
(a) In 2012 , what percent, to the nearest whole number, of the labor force was comprised of women?
\( \square \% \)
(Do not round until the final answer. Then round to the nearest integer as needed.)
Q:
A research student is working with a culture of bacteria that doubles in size every 90 minutes. The initial
population count was 1225 bacteria. Rounding to five decimal places, write an exponential function,
\( P(t)=P_{0} e^{k t} \), representing this situation. To the nearest whole number, what is the population size
after 5 hours?
Q:
In a mountain range of California, the percent of moisture that falls as snow rather than rain can be approximated by
the function p(hi) \( =76 \ln (h)-597 \), where \( h \) is the altitude in feet and p(h) is the percent of an annual snow fall at the
altitude \( h \). Use the function to approximate the amount of snow at the altitudes 5000 feet and 9000 feet.
The percent of annual precipitation that falls as snow at 5000 feet is approximately \( \square \% \).
(Round to the nearest integer.)
Q:
5. A research student is working with a culture of bacteria that doubles in size every 90 minutes. The initial
population count was 1225 bacteria. Rounding to five decimal places, write an exponential function,
\( P(t)=P_{0} e^{k t} \), representing this situation. To the nearest whole number, what is the population size
after 5 hours?
Q:
5. a) Graph the function \( f(x)=-2(x-3)^{2}+4 \),
and state its domain and range. \( D=\{x \in \mathbb{R}\} R=\{y \in \mathbb{R} \mid \)
b) What does \( f(1) \) represent on the graph?
Indicate, on the graph, how you would find
\( f(1) \).
Q:
\[ f(x)=5(0.2)^{x} \]
\( O a=0.2 ; b=5 ; \) exponential growth
\( O a=5 ; b=0.2 ; \) exponential growth
\( O a=5 ; b=0.2 ; \) exponential decay
\( O_{a}=0.2 ; b=5 ; \) exponential decay
Q:
Determine whether the function below represents exponential growth or exponential decay.
\[ y=12 \cdot\left(\frac{17}{10}\right)^{x} \]
Q:
Use transformations of the graph of \( f(x)=2^{x} \) to graph the given function. Be sure to graph
and give the equation of the asymptote. Use the graph to determine the function's domain
and range. If applicable, use a graphing utility to confirm your hand-drawn graphs.
\( h(x)=2^{x-2}-1 \)
Graph \( h(x)=2^{x-2}-1 \) and its asymptote. Graph the asymptote as a dashed line. Use the
graphing tool to graph the function.
Q:
Determine whether the function below represents exponential growth or exponential decay.
\[ \begin{array}{l}\text { (Hint: 1st identify which part of your function determines if you have a growth or decay.) } \\ \qquad y=2 \cdot(0.75)^{x}\end{array} \]
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