Exponential and Logarithmic Functions — Test

Question 10 • Algebra 2 with Probability

Which table represents an exponential function of the form y is equal to b to the x th power when 0 is less than b comma b is less than 1 ?

Answer

Table with 2 columns and 8 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 3'; Column 2, '1 over 27' Row 3: Column 1, 'negative 2'; Column 2, '1 ninth' Row 4: Column 1, 'negative 2'; Column 2, '1 third' Row 5: Column 1, '0'; Column 2, '1' Row 6: Column 1, '1'; Column 2, '3' Row 7: Column 1, '2'; Column 2, '9' Row 8: Column 1, '3'; Column 2, '27'

Table with 2 columns and 8 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 2 point 7 5'; Column 2, 'negative 1 point 3 8 6' Row 3: Column 1, 'negative 2 point 5'; Column 2, 'negative 0 point 6 9 3' Row 4: Column 1, 'negative 2'; Column 2, '0' Row 5: Column 1, 'negative 1'; Column 2, '0 point 6 9 3' Row 6: Column 1, '0'; Column 2, '1 point 0 9 9' Row 7: Column 1, '1'; Column 2, '1 point 3 8 6' Row 8: Column 1, '2'; Column 2, '1 point 6 0 9'

Table with 2 columns and 8 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 3'; Column 2, '27' Row 3: Column 1, 'negative 2'; Column 2, '9' Row 4: Column 1, 'negative 1'; Column 2, '3' Row 5: Column 1, '0'; Column 2, '1' Row 6: Column 1, '1'; Column 2, '1 third' Row 7: Column 1, '2'; Column 2, '1 ninth' Row 8: Column 1, '3'; Column 2, '1 over 27'

Table with 2 columns and 8 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 2 point 7 5'; Column 2, '1 point 3 8 6' Row 3: Column 1, 'negative 2 point 5'; Column 2, '0 point 6 9 3' Row 4: Column 1, 'negative 2'; Column 2, '0' Row 5: Column 1, 'negative 1'; Column 2, 'negative 0 point 6 9 3' Row 6: Column 1, '0'; Column 2, 'negative 1 point 0 9 9' Row 7: Column 1, '1'; Column 2, 'negative 1 point 3 8 6' Row 8: Column 1, '2'; Column 2, 'negative 1 point 6 0 9'

Explanation

For y = b^x with 0 < b < 1, the values decrease as x increases. In table B, each step to the right multiplies y by 1/3: for example, y is 1 when x = 0 and 1/3 when x = 1, so the function is y = (1/3)^x. The other tables do not show this pattern.

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