Tema
Q:
A wooden artifact from an ancient tomb contains 40 percent of the carbon-14 that is present in living trees.
How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.)
years
Q:
2. Domonstre por indução matemática que, para todo intelro positivo \( n \), é válida a proprosição \( P(n) \) :
\( \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots+\frac{1}{2^{n}}=1-\frac{1}{2^{n}} \)
Q:
2) \( f(x)=\frac{x^{2}+x}{3 x^{2}-12} \)
Q:
Evaluate or simplify the expression without using a calculator.
\( e^{\ln 3 x^{3}} \)
\( e^{\ln 3 x^{3}}=\square \)
Q:
Evaluate or simplify the expression without using a calculator.
\( e^{\ln 146} \)
Q:
27 Multiple Choice 1 point
Solve the problem.
The population of an animal species in a certain area is modeled by \( \mathbf{F}(\mathrm{t})=400 \mathrm{log}(2 t+3) \) where \( t \) is the time in months since the species was introduced to the area. Find the
population of this species in the area 6 months after the species is introduced.
74
704
240
Q:
6. Graph \( y=\log _{\frac{1}{2}}(x)+ \) 2. Analyze the function where \( 0<b<1 \).
Domain:
Range:
\( \lim _{x \rightarrow 0^{+}} f(x) \)
Q:
Find the vertical and horizontal asymptotes for \( g(x)=\frac{\sqrt{x^{2}-4}}{2-x} \)
Q:
Hence, determine a general formula for the pattern \( 0 ;-6 ;-20 ;-42 \ldots \)
Simplify your answer as far as possible.
ESTION 4
c) \( =-2 x^{2}+2 \) and \( g(x)=2^{x}+1 \) are the defining equations of graphs \( f \) and \( g \) respectively.
Write down an equation for the asymptote of \( g \).
Sketch the graphs of \( f \) and \( g \) on the same set of axes, clearly showing ALL
intercepts with the axes, turning points and asymptotes.
Write down the range of \( f \).
Determine the maximum value of \( h \) if \( h(x)=3 /(x) \).
What transformation does the graph of \( y=f(x) \) undergo in order to obtain the
Q:
11
A ball is dropped from a height of 10 feet. The ball repeatedly bounces, and the maximum height of the ball
after each bounce is \( 20 \% \) less than the previous maximum height. Which of the following arguments is
correct regarding a sequence that can be used to model the successive maximum heights, in feet?
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