Decide whether each representation is best described by a quadratic, exponential, or logarithmic function.
If the function is exponential, find the base (also called the growth factor): How much does y increase (2x? 10x?) for a single increase in x?
If the function is logarithmic, find the base: How much does x need to increase (2x? 10x?) just to get a single increase in y?
HINT: Can you draw the arrows to calculate the first difference? The second? What does it mean if neither one is constant?
| x |
y |
1 |
0 |
10 |
1 |
100 |
2 |
1000 |
3 |
10000 |
4 |
100000 |
5 |
1000000 |
6 |
|
| x |
y |
0 |
1 |
1 |
10 |
2 |
100 |
3 |
1000 |
4 |
10000 |
5 |
100000 |
6 |
1000000 |
|
| x |
y |
70 |
-169 |
71 |
-126 |
72 |
-81 |
73 |
-34 |
74 |
15 |
75 |
66 |
76 |
119 |
|
| x |
y |
5 |
1 |
10 |
2 |
20 |
3 |
40 |
4 |
80 |
5 |
160 |
6 |
320 |
7 |
|
| x |
y |
-3 |
36 |
-2 |
16 |
-1 |
4 |
0 |
0 |
1 |
4 |
2 |
16 |
3 |
36 |
|
| x |
y |
1 |
0 |
6 |
1 |
36 |
2 |
216 |
3 |
1296 |
4 |
7776 |
5 |
466656 |
6 |
|
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