Topic
Q:
Use the exponential decay model, \( A=A_{0} e^{\mathrm{kt}} \), to solve the following.
The half-life of a certain substance is 22 years. How long will it take for a sample of this substance to decay to \( 90 \% \) of its original amount?
It will take approximately \( \square \)
(Round to one decimal place as needed.)
Q:
Assigning lower quotas, the following percentages add up to \( 99 \% \). Using the Hamilton Method, which of them gets its
upper quota?
\( 12.471 \% \)
\( 33.849 \% \)
\( 41.179 \% \)
\( 13.825 \% \)
Q:
75-78 ■ Encuentre las funciones \( f \circ g \) y \( g \circ f y \) sus dominios.
75. \( f(x)=2^{x}, \quad g(x)=x+1 \)
77. \( f(x)=\log _{2} x, \quad g(x)=x-2 \)
Q:
05) Um fabricante pode produzir calcados ao custo de \( R \$ 20,00 \) o par.
Estima-se que, se cada par for vendido por \( x \) reais, o fabricante venderá
por mês \( 80-x(0 \leq x \leq 80) \) pares de sapatos. Assim, o lucro mensal do
fabricante é uma função do preço de venda. Qual deve ser o preço de
venda, de modo que o lucro mensal seja máximo?
Q:
\[ f(x)=3-3^{x+1} \]
Parent Function:
Transformations:
Q:
Se designarmos por \( [3 ; 4] \) o intervalo fechado, em
IR, de extremidades 3 e 4 , é correto escrever:
Selecione uma opção:
a. \( \quad\{3,4\} \cup[3 ; 4]= \) ir
b. \( \quad\{3,4\} \subset[3 ; 4] \)
c. \( \quad\{3,4\}=[3 ; 4] \)
d. \( \quad\{3,4\} \in[3 ; 4] \)
Q:
Given the function: \( h(x)=-\frac{2}{x-2}+2 \).
\( 5.1 \quad \) Write down the equations of the asymptotes of \( h \).
\( 5.2 \quad \) Draw the graph of \( h \). Clearly show all asymptotes and intercepts with the axes.
\( 5.3 \quad \) Determine the equation of the axis of symmetry of \( h \) with \( m<0 \).
Q:
Using Descartes' Rule of signs, how many positive real zeros sh
\[ f(x)=-x^{3}+2 x^{2}-4 x+1 \text { ? } \]
\( \begin{array}{ll}\text { a. } 3 & \text { c. } 2 \\ \text { b. } 3 \text { or } 1 & \text { d. } 2 \text { or } 0\end{array} \)
Q:
Example 4:
You are interested in two second-hand gaming consoles. The first console's price is
given by the function \( f(t)=600(0.75)^{t} \), and the second console's price is given
by \( g(t)=800(0.6)^{t} \), where \( t \) represents the time in years. Your budget
constraints require you to choose the more affordable option within the next 2
years.
Which statement below best represents the outcome?
- You buy the first console.
- You buy the second console.
Q:
Example 4:
You are interested in two second-hand gaming consoles. The first console's price is
given by the function \( f(t)=600(0.75)^{t} \), and the second console's price is given
by \( g(t)=800(0.6)^{t} \), where \( t \) represents the time in years. Your budget
constraints require you to choose the more affordable option within the next 2
years.
Which statement below best represents the outcome?
- You buy the first console.
- You buy the second console.
- Both consoles cost the same amount.
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