the table below shows values for function L (d) = 12 /d + 4 the function models the number of likes that maras video received on day d after she first posted it to her blog. Describe how the average rate of change in the values of L(d) over successive intervals varies in the context of this situation d= days L=likes. D- 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16. L(d)- 16,21,25,28,31,33,36,38,40,42,44,46,47,49,50,52
To determine how the average rate of change in the values of L(d) varies over successive intervals, we can calculate the rate of change between each pair of consecutive values of L(d).
Let's calculate the rate of change between each pair of consecutive values of L(d) using the given table:
- The rate of change between (D1, L1) and (D2, L2) is:
(D2 - D1) / (L2 - L1) = (2 - 1) / (21 - 16) = 1/5
- The rate of change between (D2, L2) and (D3, L3) is:
(D3 - D2) / (L3 - L2) = (3 - 2) / (25 - 21) = 1/4
- The rate of change between (D3, L3) and (D4, L4) is:
(D4 - D3) / (L4 - L3) = (4 - 3) / (28 - 25) = 1/3
- The rate of change between (D4, L4) and (D5, L5) is:
(D5 - D4) / (L5 - L4) = (5 - 4) / (31 - 28) = 1/3
- The rate of change between (D5, L5) and (D6, L6) is:
(D6 - D5) / (L6 - L5) = (6 - 5) / (33 - 31) = 1/2
- The rate of change between (D6, L6) and (D7, L7) is:
(D7 - D6) / (L7 - L6) = (7 - 6) / (36 - 33) = 1/3
- The rate of change between (D7, L7) and (D8, L8) is:
(D8 - D7) / (L8 - L7) = (8 - 7) / (38 - 36) = 1/2
- The rate of change between (D8, L8) and (D9, L9) is:
(D9 - D8) / (L9 - L8) = (9 - 8) / (40 - 38) = 1/2
- The rate of change between (D9, L9) and (D10, L10) is:
(D10 - D9) / (L10 - L9) = (10 - 9) / (42 - 40) = 1/2
- The rate of change between (D10, L10) and (D11, L11) is:
(D11 - D10) / (L11 - L10) = (11 - 10) / (44 - 42) = 1/2
- The rate of change between (D11, L11) and (D12, L12) is:
(D12 - D11) / (L12 - L11) = (12 - 11) / (46 - 44) = 1/2
- The rate of change between (D12, L12) and (D13, L13) is:
(D13 - D12) / (L13 - L12) = (13 - 12) / (47 - 46) = 1
- The rate of change between (D13, L13) and (D14, L14) is:
(D14 - D13) / (L14 - L13) = (14 - 13) / (49 - 47) = 1/2
- The rate of change between (D14, L14) and (D15, L15) is:
(D15 - D14) / (L15 - L14) = (15 - 14) / (50 - 49) = 1
- The rate of change between (D15, L15) and (D16, L16) is:
(D16 - D15) / (L16 - L15) = (16 - 15) / (52 - 50) = 1/2
From the calculations, we can observe that the average rate of change in the values of L(d) varies over successive intervals:
- The average rate of change is 1/5 for the first interval.
- The average rate of change increases to 1/4 in the second interval and remains constant for the next two intervals (third and fourth).
- The average rate of change increases to 1/2 in the fifth interval and remains constant for the next three intervals (sixth, seventh, and eighth).
- The average rate of change increases to 1 in the twelfth interval and then decreases to 1/2 in the fourteenth and sixteenth intervals.
Overall, the average rate of change in the values of L(d) varies, sometimes increasing and sometimes remaining constant, depending on the specific intervals considered.