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 14 12 point 6 11 point 3 4 10 point 2 0 6 9 point 1 8 5
Answer
A
Exponential; y is equal to 14 times 0 point 1 0 to the x th power
B
Linear; y is equal to negative 1 point 2 0 2 4 x plus 13 point 8 7 1
C
Linear; 18 point 8 7 1 x minus 1 point 2 0 2 4
D
Exponential; y is equal to 14 times 0 point 9 0 to the x th power
Explanation
The values are multiplied by about 0.90 each time x increases by 1: 12.6 ÷ 14 = 0.9, and 11.34 ÷ 12.6 = 0.9. A constant ratio indicates an exponential function. Since f(0) = 14, a possible formula is y = 14(0.90)^x, which is choice B.
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