2. The population of a town is modelled by the function
\( P ( t ) = 6 t ^ { 2 } + 110 t + 4000 \) , where \( P ( t ) \) is the population and \( t \) is the time in years since \( 2000 \) . a) What will the population be in \( 2020 \) ? b) When will the population be \( 6000 \) ? c) Will the population ever be 0? Explain your answer.
a)2020-2000=20=t p（400）=8400
b)t\(\approx 30\)
c)yes Because the minimum value is 4000
9. A board game company models the profit on its latest board game using the quadratic relation
\( P = - 2 x ^ { 2 } + 28 x - 90 , \) where \( x \) is the number of games it produces in hundred thousands and \( P \) is the profit in millions of dollars.
a) What are the break-even points for the company?
b) What is the maximum profit that the company can earn?
The graph of \( y = f ( x ) \) is stretched horizontally by a factor of \( 5 \) , and reflected in the \( x \) -axis. What is the equation of the image graph in terms of \( f \) ?
A. \( y = - f ( 5 x ) \) C. \( y = - f ( \frac { 1 } { 5 } x ) \)
B. \( y = - \frac { 1 } { 5 } f ( x ) \) D. \( y = - 5 f ( x )\)
