1. Emily filled an empty horse trough with water. The water level, in centimeters, is proportional to time elapsed, in minut
es, since she began filling the trough. The graph shows this relationship.
(a) What
rate does the point 8,28 represent?
Explain.
(b) What
is the unit rate for the situation in terms of centimeters/minute? Explain.
(c) Explain
how the points 8,28 and 6,21 show that the water
level varies directly with the time elapsed.
1 answer:
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Answer:
Step-by-step explanation:
<u>Key skills needed: Explicit formula, Geometric sequence</u>
1) This is a geometric sequence, meaning a constant (like 6 or 3.5) is being multiplied to every term. First we need to find the constant.
This can be done by doing -42 ÷ 7 or 252 ÷ -42
-42 ÷ 7 equals -6.
252 ÷ -42 also equals -6.
2) This means that constant is -6.
3) The general form for an explicit formula of a geometric sequence is:
--> r means the constant (or common ratio) that is being multiplied.
--> means the first term
--> means the "nth" numbered term (so
is the 3rd term,
is the 10th term and so on).
--> is just the "n" in
minus 1.
4) We can use this formula to create an explicit formula for the geometric sequence in the problem.
--> (Since we got -6 as the constant/common ratio).
--> (Since 7 is the 1st term)
This means that our formula would be -->
<em>Hope you understood and have a nice day!! :D</em>