Question

david played a slot machine.
w(t) models his winnings (in dollars, where a negative number means david is losing) as a function of time t (in hours).
when did davids winnings decrease faster?
choose 1 answer:
between 1 and 4.5 hours since he started playing
between 4.5 and 6 hours since he started playing
the winnings decreased at the same rate over both intervals

Explanation:

Step1: Calculate the rate of change for the first interval

The formula for the average rate of change is $\frac{W(t_2)-W(t_1)}{t_2 - t_1}$.
For the interval $t_1 = 1$ and $t_2=4.5$, $W(t_1) = 80$ and $W(t_2)=10$.
The rate of change is $\frac{10 - 80}{4.5-1}=\frac{-70}{3.5}=-20$.

Step2: Calculate the rate of change for the second interval

For the interval $t_1 = 4.5$ and $t_2 = 6$, $W(t_1)=10$ and $W(t_2)=-41$.
The rate of change is $\frac{-41 - 10}{6 - 4.5}=\frac{-51}{1.5}=-34$.

Answer:

B. Between 4.5 and 6 hours since he started playing