This table belongs to an exponential function.
There is a second difference of 4.
Lauren is saving money for a new sweater. Every Sunday she counts and records the number of dollars in her piggy bank and notices that these amounts resemble a function, f(x), where x is the number of weeks since she started saving and f (x) is the amount of money in the piggy bank at the end of that week, The table of values for the function, f (x), is given below.
0-5
1-8
2-13
3-20
4-29
this table belongs to a
linear
quadratic
exponential
function.
there's is a
first
second
third
difference of
2
3
4
5 answers
are you sure?
I apologize for the error in my previous response. Let's recheck the table of values.
To determine the type of function, we need to look at the differences between consecutive values of f(x):
8 - 5 = 3
13 - 8 = 5
20 - 13 = 7
29 - 20 = 9
The differences between consecutive values are not constant, so it is not a linear function. Let's check the second differences:
5 - 3 = 2
7 - 5 = 2
9 - 7 = 2
The second differences are constant, so it is a quadratic function.
Therefore, the table of values belongs to a quadratic function, and the second difference is 2. Thank you for your patience.
To determine the type of function, we need to look at the differences between consecutive values of f(x):
8 - 5 = 3
13 - 8 = 5
20 - 13 = 7
29 - 20 = 9
The differences between consecutive values are not constant, so it is not a linear function. Let's check the second differences:
5 - 3 = 2
7 - 5 = 2
9 - 7 = 2
The second differences are constant, so it is a quadratic function.
Therefore, the table of values belongs to a quadratic function, and the second difference is 2. Thank you for your patience.
explain this
To determine the type of function from a set of values, we can look at the differences between consecutive values and check if they follow a pattern. In this case, we start by looking at the first differences between consecutive values of f(x):
8 - 5 = 3
13 - 8 = 5
20 - 13 = 7
29 - 20 = 9
The first differences are not constant (3, 5, 7, 9), which indicates that the function is not linear. We then check the second differences by looking at the differences between consecutive first differences:
5 - 3 = 2
7 - 5 = 2
9 - 7 = 2
Since the second differences are constant (2), this indicates that the function is quadratic. The constant second difference is a characteristic of quadratic functions.
Therefore, based on the pattern of differences in the values provided in the table, we can conclude that the function represented by the table is a quadratic function, and the second difference is 2.
8 - 5 = 3
13 - 8 = 5
20 - 13 = 7
29 - 20 = 9
The first differences are not constant (3, 5, 7, 9), which indicates that the function is not linear. We then check the second differences by looking at the differences between consecutive first differences:
5 - 3 = 2
7 - 5 = 2
9 - 7 = 2
Since the second differences are constant (2), this indicates that the function is quadratic. The constant second difference is a characteristic of quadratic functions.
Therefore, based on the pattern of differences in the values provided in the table, we can conclude that the function represented by the table is a quadratic function, and the second difference is 2.