Precálculo preguntas y respuestas

Write the equation of the hyperbola \( 4 x^{2}-25 y^{2}+8 x+250 y-721=0 \) in standard form \[ \begin{array}{l}\text { Where: } \\ h=\square \\ k=\square \\ \mathrm{a}=\square \\ \mathrm{b}=\square\end{array} \]

Write an exponential function that has a base of \( e \) and passes through the point (0, 1).

Exercice 3 La population d'une ville augmente régulièrement de \( 10 \% \) par an. En 2019 , elle était de 8000 habitants. On désigne par \( \left(u_{n}\right) \) le nombre théorique d'habitants estimé pour l'année \( (2019+n) \). On a donc \( u_{0}=8000 \). 1. Calculer les termes \( u_{1}, u_{2} \) et \( u_{3} \). Détailler les calculs. 2. Ecrire la relation de récurrence reliant les termes \( u_{n+1} \) et \( u_{n} \). 3. En déduire la nature de la suite. 4. A l'aide de la calculatrice, calculer le nombre d'habitants prévus en 2026. 5. A l'aide de la calculatrice, déterminer en quelle année la population aura doublé. Justifier.

3. (2 points) Find an exponential function that fits: A function that represents the doubling of \( \$ 1000 \) over 7 years.

With each heartbeat, blood pressure increases as the heart contracts, then decreases as the heart rests between beats. The maximum blood pressure is called the systolic pressure and the minimum blood pressure is called diastolic pressure. When a doctor records an individual's blood pressure such as " 120 over 80 " it is understood as "systolic over diastolic". Suppose that the blood pressure for a certain individual is approximated by \( p(t)=60+30 \) sin ( \( 160 \pi t) \) where \( p \) is the blood pressure in mmHg (millimeters of mercury) and \( t \) is the time in minutes after recording begins. (a) Find the period of the function and interpret the results. (b) Find the maximum and minimum values and interpret this as a blood pressure reading. (c) Find the times at which the blood pressure is at its maximum. Part: \( 0 / 3 \) Part 1 of 3 (a) Find the period of the function and interpret the results. The period is minutes and represents the time for one complete heartbeat. This implies that the heart rate is beats per minute. (Write your answers as simplified fractions, if necessary.)

Realiza la gráfica de la función: \[ y=-\frac{1}{2} x^{2}-2 x+6 \]

The functions \( f \) and \( g \) are defined as follows. \[ f(x)=\frac{x+3}{x^{2}-9} \] \[ g(x)=\frac{x+4}{x^{2}-8 x+16} \] Write each answer as an interval or union of intervals. Domain of \( f: \square \) Domain of \( g: \square \)

Cl dominio de \( f(x)=\ln \left(x^{2}+4\right) \) es

4. (2 points) For \( f(x)=\frac{x^{2}+x-6}{x^{2}-9}=\frac{(x-2)(x+3)}{(x+3)(x-3)} \) Find any/all asymptotes

A population of bacteria is growing according to the equation \( P(t)=1950 e^{0.17 t} \). Use a graphing calculator to estimate when the population will exceed 6861 . \( t=\square \) Give your answer accurate to one decimal place.