Exponential Functions Quiz

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

• 400 decks per day

• 200 decks per day

• 100 decks per day

• 50 decks per day

Tags

TEKS.MATH.A.3B

TEKS.MATH.8.4C

Calculate the average rate of change for the following intervals: b. day 15 to day 20.

• 100 decks per day

• 150 decks per day

• 200 decks per day

• 250 decks per day

Tags

TEKS.MATH.A.3B

TEKS.MATH.8.4C

A study was conducted to analyze the 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 · b^t, and the population is increasing, select all statements that must be true.

• A. b > 1

• B. b < 1

• C. 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.

• D. 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.

• E. a > 0

Tags

TEKS.MATH.A.9C

Function $ f $ models the population, in thousands, of a city $ t $ years after 1930. 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?

• Yes, because it provides a simple average over the entire period.

• No, because it does not account for variations in population growth.

• Yes, because it accurately reflects the population trend.

• No, because it is not based on actual population data.

Tags

TEKS.MATH.A.3B

TEKS.MATH.8.4C

The function, $ f $, gives the number of copies a book has sold $ w $ weeks after it was published. The equation $ f(w) = 500 \cdot 2^w $ defines this function. Select all domains for which the average rate of change could be a good measure for the number of books sold.

• 0 ≤ w ≤ 2

• 0 ≤ w ≤ 7

• 5 ≤ w ≤ 7

• 5 ≤ w ≤ 10

• 0 ≤ w ≤ 10

Tags

TEKS.MATH.A.3B

TEKS.MATH.8.4C

The graph shows a bacteria population decreasing exponentially over time. The equation $ p = 100,000,000 \cdot \left( \frac{2}{3} \right)^h $ gives the size of a second population of bacteria, where $ h $ is the number of hours since it was measured at 100 million. Which bacterial population decays more quickly?

• The population shown in the graph

• The population described by the equation

• Both populations decay at the same rate

• It cannot be determined from the given information

Tags

TEKS.MATH.AR.3A

Technology required. A moth population, $ p $, is modeled by the equation $ p = 500,000 \cdot \left( \frac{1}{2} \right)^w $, where $ w $ is the number of weeks since the population was first measured. What was the moth population when it was first measured?

• 500,000

• 250,000

• 125,000

• 62,500

Tags

TEKS.MATH.A.9C

TEKS.MATH.2A.5B

Technology required. A moth population, $ p $, is modeled by the equation $ p = 500,000 \cdot \left( \frac{1}{2} \right)^w $, where $ w $ is the number of weeks since the population was first measured. Use technology to graph the population and find out when it falls below 10,000.

• After 5 weeks

• After 6 weeks

• After 7 weeks

• After 8 weeks

Tags

TEKS.MATH.A.9C

TEKS.MATH.2A.5B

Give a value for $ r $ that would indicate that a line of best fit has a positive slope and the variables are strongly correlated.

• 0.1

• 0.5

• 0.9

• 1.0

Tags

TEKS.MATH.AR.7B

The size of a district and the number of parks in it have a weak positive relationship. What does it mean to have a weak positive relationship in this context?

• The number of parks increases significantly with the size of the district.

• The number of parks decreases as the size of the district increases.

• There is a slight increase in the number of parks as the size of the district increases.

• The size of the district and the number of parks are not related.

Tags

TEKS.MATH.A.3B