Question

por favor me ajudem aee 71 pontos

Answer 1

a) $f(x)=3^{x}$

Crescente.

b) $f(x)=\left(\dfrac{2}{5}\right)^{x}$.

Decrescente.

c) $f(x)=2^{x-1}$

Crescente.

a) $2^{x}=64~~\Rightarrow~~2^{x}=2^6~~\Rightarrow~~\boxed{x=6}$.


b) $3^{x-2}=9~~\Rihtarrow~~3^{x-2}=3^2~~\Rightarrow~~x-2=2~~\Rightarrow~~\boxed{x=4}$.


c) $5^{x^2-2x}=125~~\Rightarrow~~5^{x^2-2x}=5^3~~\Rightarrow~~x^2-2x=3~~\Rightarrow~~x^2-2x-3=0$.

$\Delta=(-2)^2-4\cdot1\cdot(-3)=4+12=16$

$x=\dfrac{-(-2)\pm\sqrt{16}}{2}=\dfrac{2\pm4}{2}=1\pm2$

$x'=1+2=3$ e $x"=1-2=-1$.


d) $3^{x-5}=27^{1-x}~~\Rightarrow~~3^{x-5}=(3^3)^{1-x}~~\Rightarrow~~3^{x-5}=3^{3-3x}$

$x-5=3-3x~~\Rightarrow~~3x+x=3+5~~\Rightarrow~~4x=8~~\Rightarrow~~x=2$.


3) $M(t)=50.000\cdot(1,1)^{t}$

a) 3 meses.

$M(3)=50.000\cdot(1,1)^3=50.000\cdot1,331=66~550$

b) 6 meses.

$M(6)=50.000\cdot(1,1)^6=50.000\cdot1,771561=88~578,05$

c) 1 ano = 12 meses.

$M(12)=50.000\cdot(1,1)^{12}\approx156,921,42$.

Answer 2

1)
Uma função exponencial do tipo:  $f(x)=a^x$ é crescente se a>1 e é decrescente se 0<a<1

Logo são crescentes as funções de letras: a e c e decrescente a função de letra b

Seus gráficos estão anexos.

2)
$2^x=64\\ \\ 2^x=2^6\\ \\ \boxed{x=6}$

$3^{x-2}=9\\ \\ 3^{x-2}=3^2\\ \\ x-2=2\\ \\ x=4$

$5^{x^2-2x}=125\\ \\ 5^{x^2-2x}=5^3\\ \\ x^2-2x=3\\ \\ x^2-2x-3=0\\ \\ \Delta=(-2)^2-4.1.(-3)=4+12=16\\ \\ x=\frac{2\pm4}{2}\\ \\ S=\{-1,3\}$

$3^{x-5}=27^{1-x}\\ \\ 3^{x-5}=(3^3)^{1-x}\\ \\ 3^{x-5}=3^{3-3x}\\ \\ x-5=3-3x\\ \\ 4x=8\\ \\ x=2$

3)
$M(t)=50000(1,1)^t\\ \\ M(3)=50000.(1,1)^3=50000.(1,331)=66550,00\\ \\ M(6)=50000.(1,1)^6=5000.(1,771561)=88578,00\\ \\ M(12)=50000.(1,1)^{12}=50000.(3,1384)=156921,40$