Given the table, determine if the data represents a linear or an exponential function and find a possible formula for the function. x 0 1 2 3 4 f of x 12 point 5 13 point 7 5 15 point 1 2 5 16 point 6 3 8 18 point 3 0 1
Answer
A
Linear; 12 point 3 6 4 8 x plus 1 point 4 9 9
B
Linear; y is equal to 1 point 4 9 9 x plus 12 point 3 6 4 8
C
Exponential; y is equal to 1 point 1 0 times 12 point 5 to the x th power
D
Exponential; y is equal to 12 point 5 times 1 point 1 0 to the x th power
Explanation
The values increase by a factor of about 1.10 each time: 13.75 ÷ 12.5 = 1.10, and 15.125 ÷ 13.75 = 1.10. A constant multiplicative change indicates an exponential function. Since f(0) = 12.5, a possible formula is y = 12.5 × 1.10ˣ, the exponential choice with initial value 12.5.
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