5.10.5 Practice

Complete the following questions to practice the skills you have learned in this lesson.

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 $d$.
   
   

   $t$	$d(t)$
   0	2,000
   5	1,283
   10	823
   15	528
   20	338

   
   Calculate the average rate of change for the following intervals:
   
   
1. day 0 to day 5

2. day 15 to day 20

2. A study was conducted to analyze the effects on deer population in a particular area. Let $f$ be an exponential function that gives the population of deer $t$ years after the study began.
   If $f(t)=a\cdot <!--\; \cdot \; -->b^t$ and the population is increasing, select three statements that must be true.;

1. $b>1$
3. The average rate of change from year 0 to year 5 is less than the average rate of change from year 10 to year 15.
4. The average rate of change from year 0 to year 5 is greater than the average rate of change from year 10 to year 15.
5. $a>0$

3. Function $f$ models the population, in thousands, of a city $t$ years after 1930.
   
   1. The average rate of change of $f$ from $t=0$ to $t=70$ is approximately 14 thousand people per year. Is this value a good way to describe the population change of the city over that time period?

1. No
2. Yes

2. The rate of change between years 1940 and 1950 is greater than/less than the rate of change between years 1960 and 1970.

1. less than
2. greater than

4. The function, $f$, gives the number of copies of a book that have sold $w$ weeks after it was published. The equation $f(w)=500\cdot <!--\; \cdot \; -->2^w$ defines this function. Select two domains for which the average rate of change could be a good measure for the number of books sold.

1. $0\le <!--\; \le \; -->w\le <!--\; \le \; -->2$
2. $0\le <!--\; \le \; -->w\le <!--\; \le \; -->7$
3. $5\le <!--\; \le \; -->w\le <!--\; \le \; -->7$
4. $5\le <!--\; \le \; -->w\le <!--\; \le \; -->10$
5. $0\le <!--\; \le \; -->w\le <!--\; \le \; -->10$

5. The moth population over 10 weeks is graphed below.
   
   1. After 4 weeks, the population was 40 thousand. What was the average rate of change from the start to the 4th week? Do not enter commas in your answer.

2. The rate of change between weeks 1 and 2 is greater than/less than the rate of change between weeks 3 and 4.

1. less than
2. greater than