Math 110 Course Resources - Exponential \& Logarithmic Functions Course Packet on logistic growth If the population of squirrels on campus \( t \) years after the beginning of 1855 is given by the logistic growth function \( s(t)=\frac{3000}{1+12 e^{-1.08 t}} \) find the time \( t \) such that \( s(t)=2400 \). Time, \( t=\square \)

Determina il dominio D e la funzione inversa nell'intervallo \( (3,+\infty) \) della funzione: \( \quad y=\ln \left(\frac{3 x^{2}}{x^{2}-9}\right) \)

Donner la négation de chacune des propositions suivantes: (a) \( (\forall x \in \mathbb{R})(\exists n \in \mathbb{Z}) / n \leq x<n+1 \). (b) \( (\exists x \in \mathbb{R})(\forall n \in \mathbb{Z})[x<n \) ou \( x \geq n+1] \). (c) \( (\exists x \in \mathbb{R}) /-1<x<2 \Rightarrow|x| \geq 2 \). (d) \( \left(\forall x \in \mathbb{R}^{+}\right)\left(\forall y \in \mathbb{R}^{+}\right) x+y=0 \Rightarrow x=y=0 \).

Given the function with the equation \( k(x)=\frac{-6}{x+2}-2 \) : 7.1 Write the equations of the asymptotes of \( k \). 7.2 Give the range of \( k \). 7.3 Give the domain of \( k \). 7.4 Drite the equation of the axis of symmetry, with a positive gradient. 7.5 If \( k \) is reflected over the \( x \)-axis and shifted upwards by 2 units, 7.6 give the equation of the new function, \( j(x) \), after the transformations. 7.7 In which quadrant(s) would the arms of \( k \) not be if it was sketched?

122. Постройте график функции \( y=-x^{2}+2 x+8 \) и найдите, ис- пользуя график: а) значение функции при \( x=2,5 ;-0,5 ;-3 ; \) б) значения аргумента, при которых \( y=6 ; 0 ;-2 \); в) нули функции и промежутки знакопостоянства; г) промежутки возрастания и убывания функции, область зна- чений функции.

Which graph best represents \( y=5\left(\frac{1}{3}\right)^{x} \)