6. The value of a particular used car has been decreasing at the same rate each year since \( 2010 \) . The equation \( C ( t ) = 25,000 \cdot ( 0.78 ) ^ { t } \) represents the value of the car \( C ( t ) \) , in dollars, as a function of \( t \) , the number of years since \( 2010 \) .
a. What do the numbers \( 25,000 \) and \( 0.78 \) tell us about this situation?
b. What is the percent decrease of the value of the car each year?
c. Sketch a graph of \( C \) .
25 represents the original value of the bicycle, and 0.75 represents the rate of decline per year.
\(b.22\% \)
Determine the following limits. If infinite, specify \( \infty \) or \( - \infty \) . If an answer does not exist, explain why. (NO POINTS WILL BE GIVEN IF A TABLE OF VALUES IS USED) b. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
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?
