The size \( P \) of a small herbivore population at time \( t \) (in years) obeys the function
\( P ( t ) = 600e ^ { 0.2 t } \) if they have enough food and the predator population stays constant. After how many years will the population reach \( 2400 \) ?
t\(\approx 7\)
A Ferris wheel ride can be represented by a sinusoidal function. A Ferris wheel at Armencity Theme Park has a diameter of \( 30 m \) and travels at a rate of \( 6 \) revolutions per minute in a clockwise rotation. You get on the ride from a platform \( 1 m \) above the ground at \( t = 0 \)
a) Determine the equation of the graph in the form \( H ( t ) = a \cos [ k ( t - d ) ] + c \) by finding the exact values of a. \( k \) , \( d \) , and \( c \) values.
b) If the Ferris wheel does not stop, determine the height above the ground after \( 28 s \)
A rocket was launched and its height, \( h \) , in metres, above the ground after time, \( t \) , in seconds, is represented by \( h = 11 + 10 t - 2 t ^ { 2 } \) . For how many seconds was the rocket in the air?
a.about \( 5.93 s \) c. about \( 6.64 s\)
b. about \(6.27 s\) d. about \( 7.35 s\)
Which of the following best describes the graph of \( w ( x ) = - ( x + 4 ) ^ { 2 } \) ? The image of \( f ( x ) = \)
(a)\(\square \) \( x ^ { 2 } \)\(\square \) \( x \) \(\square \) \(\sqrt { x} \)\(\square \) \(| x | \)\(\square \) \(x ^ { 3 } \)
after a (select all that apply)
(b)
\(\square \) reflection across the \(x\) -axis
\(\square \) translation \( 4 \) units up
\(\square \) vertical compression by a factor of \( \frac { 1 } { 4 } \) units
\(\square \) vertical stretch by a factor of \(4\) units
\(\square \) translation \(4\) units to the right
\(\square \) translation \(4\) units to the left
\( \square \) translation \( 4 \) units down
\(\square \) reflection across the \(y\) -axis
Find all numbers for which the rational expression is undefined. If the rational expression is defined for all real numbers, state this.
\( \frac { y - 2 } { y ^ { 2 } - 4 } \)
A. \( \square \)(Use a comma to separate answers as needed.)
B. The rational expression is defined for all real numbers.
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Passing through \( ( 8 , - 6 ) \) and perpendicular to the line whose equation is \( y = \frac { 1 } { 2 } x + 3 \)
Write an equation for the line in point-slope form.
\( \square \)(Simplify your answer. Use integers or fractions for any numbers in the equation.)
Write an equation for the line in slope-intercept form.
\( \square \) (Simplify your answer. Use integers or fractions for any numbers in the equation.)
