SOLUTION: The value of the Conference Board Index of 10 economic indicators in the United States could be approximated by the following function of time t in months since the end of December

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Question 1196927: The value of the Conference Board Index of 10 economic indicators in the United States could be approximated by the following function of time t in months since the end of December 2002.†
E(t) =
0.2t + 135 if 6 ≤ t ≤ 15
−0.2t + 141 if 15 < t ≤ 20.
(a)
Estimate
E(10), E(16), and E(20).
E(10) =
E(16) =
E(20) =
Interpret your answers.
E(10)
means in
---Select---
of the year

Correct:
the Conference Board Index was
.
E(16)
means in
---Select---
of the year

the Conference Board Index was
.
E(20)
means in
---Select---
of the year

the Conference Board Index was
.
(b)
Sketch the graph of E. Use your graph to estimate when the index first reached 138.
t =
(c)
Use technology to generate a table of values for E(t) with
t = 6, 7, , 20.
t 6 7 8 9 10
E(t)
t 11 12 13 14 15
E(t)
t 16 17 18 19 20
E(t)

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
E%28t%29+=0.2t+%2B+135 if 6+%3C=+t+%3C=+15
E%28t%29+=+-0.2t+%2B+141 if 15+%3C+t+%E2%89%A4+20%0D%0A%0D%0A%0D%0A%28a%29%0D%0A%0D%0A%7B%7B%7Bt=10 belongs to the interval 6+%3C=+t+%3C=+15 so we use the first formula to evaluate E%2810%29+
E%2810%29+=0.2%2A10+%2B+135+=137
t=16 belongs to the interval 15+%3C+t+%3C=+20 so we use the second formula to evaluate E%2816%29
E%2816%29+=++-0.2%2A16%2B+141=137.8
t=20 belongs to the interval 15+%3C+t+%3C=+20 so we use the second formula to evaluate E%2820%29
E%2820%29+=+-0.2%2A20%2B+141=137

since starts with the end of December 2002 and time t in months, if t=10+ it means 10+months from the end of December 2002 will be October 2003
and the Conference Board Index was+137

if t=16+ it means 16 months (1 year and 4 months) from the end of December 2002 will be April 2004
and the Conference Board Index was+137.8

if t=20+ means 20+months (1 year and 8 months) from the end of December 2002 will be August 2004
and the Conference Board Index was 137


(b)

Sketch the graph of E. Use your graph to estimate when the index first reached 138.
download


t+=15



(c)
Use technology to generate a table of values for E%28t%29 with

t+| 6 | 7| 8 |9+|10
use first formula: E%28t%29+=0.2t+%2B+135
E%286%29+=0.2%2A6+%2B+135=136.2
E%287%29+=0.2%2A7+%2B+135=136.4
E%288%29+=0.2%2A8+%2B+135=136.6
E%289%29+=0.2%2A9+%2B+135=136.6
your table is:
t ....| ...6 ....| ...7.....|... 8 ....|...9.... |...10 ..|
E%28t%29| +136.2| 136.4 | 136.6 | 136.8+| 137 |

for second table use first formula, E(t) =0.2t + 135, and do same way as I did above
t|+11|+12|+13|+14|+15
E%28t%29| +.....| ....... | ..... | ....| ..... |
for third table use second formula, E%28t%29+=+-0.2t+%2B+141, and do same way as I did above

t|+16|+17|+18|+19|+20
E%28t%29| +.....| ....... | ..... | ....| ..... |