Getting Started 
Misconception/Error The student is unable to determine where the graph of the function crosses the vertical axis. 
Examples of Student Work at this Level The student:
 Attempts to compute a value using the given function but does so incorrectly.
Â
 Determines the graph will never cross the vertical axis.
Â
 Determines the graph will cross the vertical axis at (0, 1).
Â

Questions Eliciting Thinking What type of function is described in the problem?
What does the graph of an exponential function look like?
How would you describe the point where the graph crosses the vertical axis? What is this point usually called?
What is the value of the tcoordinate of the point where the graph crosses the vertical axis? 
Instructional Implications Review the concept of an intercept and be sure the student understands intercepts graphically (as points where the graph crosses the axes) and algebraically (as points containing a coordinate of zero). Guide the student to calculate g(0) and explain what this value represents in the context of the problem.
Review the basic form of an exponential function and its two parameters, initial amount and growth/decay factor. Show the student that for any exponential function (i.e.,Â ), y = a when x = 0. Consequently, a is the yintercept and the initial amount.
Provide additional linear and exponential functions and ask the student to find any intercepts. 
Moving Forward 
Misconception/Error The student is unable to determine what the gintercept indicates in the context of the problem. 
Examples of Student Work at this Level The student determines the graph crosses the vertical axis at (0, 2500). However, the student is unable to interpret these coordinates in the context of the problem. The student says this intercept indicates:
 Where the graph crosses the yaxis.
Â
 The starting amount.
Â
 The rate of growth or the growth over time.
Â
 The population.
Â

Questions Eliciting Thinking What does t represent in the context of this problem? What does g(t) represent in the context of this problem?
What are the coordinates of the point where the graph crosses the vertical axis? What does each of these coordinates represent? 
Instructional Implications Have the student write the gintercept as an ordered pair, (0, 2500). Guide the student to understand this means that t = 0 when g(t) = 2500. Remind the student that t represents the number of years since 2012 and g(t) represents the population in the community. Ask the student what year it is when t = 0 and explain that during this year, 2012, the population was 2500. Ask the student to find and interpret other points on the graph such as g(2) or g(10).
Provide additional opportunities for the student to interpret intercepts of functions in the context of realworld and mathematical problems. 
Almost There 
Misconception/Error The student does not demonstrate an understanding of how an increase in the percentage rate of growth affects the graph of the function. 
Examples of Student Work at this Level The student determines the graph crosses the vertical axis at (0, 2500) and explains it indicates that the population of the small beach community in 2012 was 2500. When explaining how an increase in the percentage rate of growth affects the graph of the function, the student says:
 The â€śslopeâ€ť would increase.
Â
 It would stretch the graph.
Â
 It would make the graph exponential.
Â

Questions Eliciting Thinking What kind of function is g? Does an exponential function have slope?
Can you describe the graph of an exponential function?
What are the two parameters of an exponential function?
How does each parameter affect the graph of the function? 
Instructional Implications Using graphing technology, have the student graph the equation from the worksheet. Discuss the parameters of this equation with the student and what they mean in the context of the problem. Have the student increase the percentage rate of growth in the equation to, for example, 20% and graph the new equation [e.g., ] along with the original one. Ask the student to compare the two graphs and describe any differences observed. Model explaining that the initial value did not change, so the gintercept remained the same; however, an increase in the percentage rate of growth causes the graph to rise more quickly. Explain what this means about changes to the population. Additionally, ask the student to calculate and compare the average rate of change over an interval such as [2, 3] for the two functions and interpret these values in the context of the problem.
Provide the student with additional exponential functions that vary by one or both parameters and ask the student to describe and compare their graphs. Then have the student use graphing technology to check his or her descriptions.
To provide an additional opportunity for the student to compare percentage rate of growth in different exponential equations, consider implementing MFAS task Exponential Growth (FLE.1.1). 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student determines the graph crosses the vertical axis at (0, 2500) and explains it indicates that the population of the small beach community in 2012 was 2500. The student continues to write that an increase in the percentage rate of change would increase the rate at which the graph rises or cause the graph to rise more rapidly.
Â 
Questions Eliciting Thinking Could population growth be linear?
How would the equation be affected if, instead of a population increase, the population of this beach community were decreasing at a rate of 15%?
To find the population in 2020, what value would need to be substituted for t in the equation?
If the population is increasing at a constant rate of 15% per year, why is the value 1.15 used in the equation? 
Instructional Implications Ask the student to explain what is happening to the graph of the function as t approaches negative infinity. Ask the student if there is any value of t for which g(t) = 0. 