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Home Question Bank Math Pre Calculus Archive 2024 November 24

Pre-calculus Questions from Nov 24,2024

Browse the Pre-calculus Q&A Archive for Nov 24,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( 1 \leftarrow \) Determine whether the given function is one-to-one. If it is one-to-one, find a formula for the \( f(x)=\sqrt{x-3} \) A. \( f^{-1}(x)=x^{2}+3, x \geq 0 \) B. \( f^{-1}(x)=(x-3)^{2} \) C. \( N^{-1}(x)=\sqrt{x+3} \) A population of bacteria is growing according to the equation \( P(t)=300 e^{0.22 t} \), where \( t \) is the number of hours. Estimate when the population will exceed 648 . \( t= \) Give your answer accurate to one decimal place. Check Answer The population of a country was 76 million in 1998 and the continuous exponential growt rate was estimated at \( 3.2 \% \) per year. Assuming that the population of the country continues to follow an exponential growth model, find the projected population in 2009. Round your answer to 1 decimal place. The approximate population in 2009 is million people While on Casey's computer, you notice that a model for a recent experiment is completed. The mo gives the temperature \( (T) \) as a function of time \( (t) \) as given below. As before, a time of \( t=0 \) represe the time of data collection, with negative values representing earlier times. Knowing Casey, they want to know the domain, range, and other information about the model. You review the model provide the information that Casey will request. \[ T(t)=\ln (6 t+36)+1.6 \] Enter the domain in interval notation. To enter \( \infty \), type infinity. The vertical asymptote is \( t=\square \) As \( t \) approaches the vertical asymptote, \( \quad T(t) \rightarrow \square \) As \( t \) approaches \( \infty \), Exercice 1 (4 points) On considère la suite définie par récurrence pour \( n \geq 0 \) \[ \left\{\begin{array}{l}u_{0}=1 \\ u_{1}=1 \\ u_{n+2}=u_{n+1}+u_{n}\end{array}\right. \] \[ \forall n \in \mathbb{N}, \quad u_{n} \leq\left(\frac{5}{3}\right)^{n} \] Montrer par récurrence la propriété suivante : \[ u_{k} \leq\left(\frac{5}{3}\right)^{k} \text { et } u_{k+1} \leq\left(\frac{5}{3}\right)^{k+1} \] Indice : Pour l'hérédité, à \( k \) fixé on suppose que les deux inégalités suivantes sont vraies The point \( \left(7, \frac{\pi}{4}\right) \) can also be represented by which of the following polar coordinates? Select all that apply. EL DOMINIO DE F-1, LA INVERSA DE \( F(x)=2+e^{-2} \) ES EL DOMINIO DEF-1, LA INVERSA DE \( F(x)=2+e^{-2} \) ES \[ y=\exp (70) x^{64} \] Si se realiza la gráfica \( \ln (y) \) vs \( \ln (x) \), con \( \ln (\cdot) \) logaritmo en base natural (a) ¿Cual es la pendiente de la recta resultante? (b) ¿Cual es el intercepto de la recta resultante? Supongamos que una población sigue un modelo de crecimiento exponencial. Si cada 10 días la población se multiplica por \( 2^{10} \). (a) ¿Cuantos días tarda la población en multiplicarse por 32 ?
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