A store receives 2,000 decks of popular trading cards. The number of decks of cards is a function, , of the number of days, , since the shipment arrived. Here is a table showing some values of .
0
2,000
5
1,283
10
823
15
528
20
338
Calculate the average rate of change for the following intervals:
day 0 to day 5
day 15 to day 20
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Problem 2
Student Task Statement
A study was conducted to analyze the deer population in a particular area. Let be an exponential function that gives the population of deer years after the study began.
If , and the population is increasing, select all statements that must be true.
Problem 3
Student Task Statement
Function models the population, in thousands, of a city years after 1930.
The average rate of change of from to 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? Explain or show your reasoning.
Graph of a function on grid, origin O. Horizontal axis, years since 1930, from 0 to 80 by 5's. Vertical axis, population in thousands, from 0 to 1,500 by 100's. Approximate Plotted coordinates as follows: 0 comma 18, 5 comma 24, 10 comma 32, 15 comma 43, 20 comma 58, 25 comma 77, 30 comma 103, 35 comma 138, 40 comma 185, 45 comma 248, 50 comma 331, 55 comma 444, 60 comma 594, 65 comma 795, 70 comma 1063, 75 comma 1423
Problem 4
Student Task Statement
The function, , gives the number of copies a book has sold weeks after it was published. The equation defines this function.
Select all domains for which the average rate of change could be a good measure for the number of books sold.
The graph shows a bacteria population decreasing exponentially over time.
The equation gives the size of a second population of bacteria, where is the number of hours since it was measured at 100 million.
Which bacterial population decays more quickly? Explain how you know.
Graph of a function on grid, origin O. Horizontal axis, time, hours, from 0 to 6 by 1's. Vertical axis, bacteria population, millions, from 0 to 300 by 50's. Plotted coordinates as follows: 0 comma 250, 1 comma 150, 2 comma 90, 3 comma 54, 4 comma 32, 5 comma 19, 6 comma 11.
Here is a graph of Han’s distance from home as he goes home from a store.
Identify the intercepts of the graph and explain what they mean in terms of Han’s distance from home.
Nonlinear graph, coordinate plane, origin O. Horizontal axis scale 0 to 10 by 5’s, labeled “time (minutes)”. Vertical axis scale 0 to 10 by 5’s, labeled “distance (miles)”. The graph begins at (0 comma 10 and ends near (10 comma 0).
