Topic
Q:
The equation \( T^{2}=A^{3} \) shows the relationship between a planet's orbital period, \( T \), and the planet's mean distance from the
sun, \( A \), in astronomical units, \( A U \). If planet \( Y \) is \( k \) times the mean distance from the sun as planet \( X \), by what factor is the
orbital period increased?
Q:
A population of bacteria is growing according to the equation \( P(t)=1250 e^{0.17 t} \), where \( t \) is the number
of hours. Estimate when the population will exceed 2266 . Give your answer accurate to one decimal place.
\( t=\square \) hours
Q:
Find the indicated value of the logarithmic function.
\( \ln \left(e^{-3}\right) \)
Q:
Graph the inverse of the function.
\( f(x)=(x+3)^{3} \)
Q:
11. Evaluate \( \ln e^{-5} \)
Q:
1) En utilisant le raisonnement par contraposée montrer que :
\[ \forall(x, y) \in \mathbb{R}^{*} ;\left(x \neq y \text { et } x y \neq 1 \Rightarrow \frac{x}{x^{2}+1} \neq \frac{y}{y^{2}+1}\right) \]
Q:
Starting with the graph of \( f(x)=2^{x} \), write the equattion of the graph that results when:
(a) \( f(x) \) is shifted 3 units upward. \( y=\square \)
(b) \( f(x) \) is shifted 8 units to the right. \( y=\square \)
(c) \( f(x) \) is reflected about the \( x \)-axis and the \( y \)-axis. \( y=\square \)
Q:
Find a formula for the exponential function passing through the points \( \left(-2, \frac{3}{16}\right) \) and \( (2,48) \).
\( y= \)
Q:
22. On considère la suite \( \left(u_{n}\right) \) définie pour tout
\( n \in \mathbb{N} \) par \( u_{0}=10 \) et \( u_{n+1}=\frac{1}{4} u_{n}+6 \).
1. Conjecturer à la calculatrice le sens de variation de
la suite \( \left(u_{n}\right) \).
2. Prouver par récurrence que \( u_{n} \geqslant 8 \) pour tout \( n \in \mathbb{N} \).
3. En déduire sur le sens de variation de la suite \( \left(u_{n}\right) \).
4. La suite \( \left(u_{n}\right) \) est-elle convergente?
Q:
Determine the vertical asymptote(s) of the function. If none exists, state that fact.
\( f(x)=\frac{8 x-3}{x-7} \)
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