Question

Uma quantidade t varia de acordo com o tempo com a função Q(t)= 1/2elevado a t . Qual o valor de t para o qual Q(t)=1/2√2?

Answer 1

Explicação passo a passo:

$\sf Q(t) = \bigg(\dfrac{1}{2}\bigg)^t$

• Qual valor de t qual qual Q(t) = 1/2√2

$\sf \dfrac{1}{2}\sqrt{2} = \bigg(\dfrac{1}{2}\bigg)^t$

$\sf 2^{-1}\sqrt{2} = \bigg(\dfrac{1}{2}\bigg)^t$

$\sf 2^{-1}*2^{\frac{1}{2}} = (2^{-1})^t$

$\sf 2^{-\frac{1}{2}} = 2^{-t}$

$\sf \backslash \!\!\! 2^{-\frac{1}{2}} = \backslash \!\!\! 2^{-t}$

$\sf - \dfrac{1}{2} = - t$

$\red{\sf t = \dfrac{1}{2}}$

Answer 2

Oie, Td Bom?!

• Se for:

$Q(t) = ( \frac{1}{2} ) {}^{t}$

$\frac{1}{2 \sqrt{2} } = ( \frac{1}{2} ) {}^{t}$

$(2 \sqrt{2} ) {}^{ - 1} = (2 {}^{ - 1} ) {}^{t}$

$(2 \: . \: 2 {}^{ \frac{1}{2} } ) {}^{ - 1} = 2 {}^{ - t}$

$(2 {}^{ \frac{2}{3} } ) {}^{ - 1} = 2 {}^{ - t}$

$2 {}^{ - \frac{3}{2} } = 2 {}^{ - t}$

• Bases iguais, iguale os expoentes.

$- \frac{3}{2} = - t$

$- t = - \frac{3}{2} \: . \: ( - 1)$

$t = \frac{3}{2}$

• Ou se for:

$Q(t) = ( \frac{1}{2} ) {}^{t}$

$\frac{1}{2} \sqrt{2} = ( \frac{1}{2} ) {}^{t}$

$2 {}^{ - 1} \: . \: 2 {}^{ \frac{1}{2} } = (2 {}^{ - 1} ) {}^{t}$

$2 {}^{ - \frac{1}{2} } = 2 {}^{ - t}$

• Bases iguais, iguale os expoentes.

$- \frac{1}{2} = - t$

$- t = - \frac{1}{2} \: . \: ( - 1)$

$t = \frac{1}{2}$

Att. Makaveli1996