1. a store receives 2,000 decks of popular trading cards. the number of decks of cards is a function, d, of…

1. a store receives 2,000 decks of popular trading cards. the number of decks of cards is a function, d, of the number of days, t, since the shipment arrived. here is a table showing some values of d. calculate the average rate of change for the following intervals: a. day 0 to day 5 b. day 15 to day 20 t d(t) 0 2,000 5 1,283 10 823 15 528 20 338

1. a store receives 2,000 decks of popular trading cards. the number of decks of cards is a function, d, of the number of days, t, since the shipment arrived. here is a table showing some values of d. calculate the average rate of change for the following intervals: a. day 0 to day 5 b. day 15 to day 20 t d(t) 0 2,000 5 1,283 10 823 15 528 20 338

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, $d$ is a function of $t$, and the average rate of change over $[t_1,t_2]$ is $\frac{d(t_2)-d(t_1)}{t_2 - t_1}$.

Step2: Calculate average rate of change for 0 to 5 days

For the interval from $t_1 = 0$ to $t_2=5$, $d(t_1)=2000$ and $d(t_2)=1283$. $\frac{d(5)-d(0)}{5 - 0}=\frac{1283 - 2000}{5}=\frac{-717}{5}=-143.4$.

Step3: Calculate average rate of change for 15 to 20 days

For the interval from $t_1 = 15$ to $t_2 = 20$, $d(t_1)=528$ and $d(t_2)=338$. $\frac{d(20)-d(15)}{20 - 15}=\frac{338 - 528}{5}=\frac{-190}{5}=-38$.

Answer:

a. -143.4 b. -38