The formula \( A=24.2 e^{0.0766 t} \) models the population of a US state, \( A \), in millions, \( t \) years after 2000 . a. What was the fopulation of the state in 2000 ? b. When will the population of the state reach 31.4 million? a. In 2000 , the population of the state was \( \square \) million. b. The population of the state will reach 31.4 million in the year \( \square \). (Round to the nearest year as needed.)

Find the outer measure of \( x \) for \( \{-5 \leq x \leq 3\} \cup\{-2 \leq x<7\} \)

Graficar en forma aproximada las siguientes funciones, hallando dominio, imagen, y las asintotas, vertical y horizontal a) \( f_{x}=\frac{3 x-3}{x+1} \) b) \( f_{x}=\frac{2}{3 x+1} \)

The formula \( A=24.2 e^{0.0766 t} \) models the population of a US state, \( A \), in millions, \( t \) years after 2000 . a. What was the fopulation of the state in 2000 ? b. When will the population of the state reach 31.4 million? a. In 2000 , the population of the state was \( \square \) million. b. The population of the state will reach 31.4 million in the year \( \square \). (Round to the nearest year as needed.)

Ouestâo 8 a, Estudos do IBGE constataram que o tempo de vida de uma população pode ser descrita pela função \( T(x)=16 \quad(250 \log x-844) \), em que \( x \) é igual a um determinado ano. Caso esse comportamento seja mantido durante muitos anos, a expectativa vida para essa população nos anos 3000 será de: (Use log3 \( =0,4 \) )

parallel to the (i) the \( x \)-axis (ii) the \( y \)-axis. Show that an equation of the parabola with focus at \( (a \cos \alpha, a \sin \alpha) \) and dir \( \cos \alpha+y \sin \alpha+a-0 \) is \( (x \sin \alpha-y \cos \alpha)^{2}=4 a(x \cos \alpha+y \sin \alpha) \)