\[ f(x)=3-3^{x+1} \] Parent Function: Transformations:

2. (2.5 pts) Demuestra que para todo número natural \( n \), \[ 1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\ldots+\frac{1}{\sqrt{n+1}} \geq \sqrt{n+1} \] ¿A partir de qué número \( n \) se empieza a cumplir la desigualdad estricta \( > \), sin el igual?

The logistic growth function \( f(t)=\frac{111,000}{1+5400 e^{-t}} \) describes the number of people, \( f(t) \), who have become ill with influenza \( t \) weaks wfter its inital outbreak in a puticular community. a) How may people became ill with the flu when the epidemic began? b) How many people were ill by the end of the fourth week? c) what is the limiting size of the population that become ill?

QUESTION 4 Given: \( f(x)=2\left(x^{2}-1\right) \) Sketch function \( f \) on the diagram sheet. Clearly show all intercepts with the axes.

Find the equation for the exponential function that passes through the points \( (2,4) \) and \( (4,11) \).

Given: \( f(x)=2\left(x^{2}-1\right) \) Sketch function \( f \) on the diagram sheet. Clearly show all intercepts with the axes.