A small island in the middle of a river is eroding away. Each year, the island has 85% of the area from the previous year. After
one year the island has an area of 10.2 thousand square yards. Graph the sequence and describe the pattern. How much of the island is left after 6 years?
1 answer:
Answer:
see the attachment for a graph
4.53 thousand square yards remain after 6 years
Step-by-step explanation:
The area can be described by an exponential equation that multiplies the area by 0.85 when the time variable increases by 1 year. Such an equation might be ...
a(t) = 10.2·0.85^(t-1)
The graph of this is attached.
After 6 years, the equation predicts
a(6) = 10.2·0.85^(6-1) ≈ 4.53 thousand square yards
of island will remain.
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Answer: OPTION A.
Step-by-step explanation:
Given the following function:
You know that it represents the the height of the ball (in meters) when it is a distance "x" meters away from Rowan.
Since it is a Quadratic function its graph is parabola.
So, the maximum point of the graph modeling the height of the ball is the Vertex of the parabola.
You can find the x-coordinate of the Vertex with this formula:
In this case:
Then, substituting values, you get:
Finally, substitute the value of "x" into the function in order to get the y-coordinate of the Vertex:
Therefore, you can conclude that:
<em> The maximum height of the ball is 0.75 of a meter, which occurs when it is approximately 1 meter away from Rowan.</em>