Exercise 69 Page 316

Practice makes perfect

a To draw a graph on our calculator, we first have to press

Y =

and type the function in one of the rows. Having typed the function, we can press

GRAPH

to draw it. While we are typing the function, we should replace

A

and

s

with

x

and

y,

respectively.

Next, we will restrict the domain such that $200 \leq A \leq 35000 .$ To do that we will press $2nd$ and $MATH .$ Then, we will use the fourth option and sixth option in the TEST column and first option in the LOGIC column.

With this, the domain can be restricted as shown below.

b To estimate the number of species in a lake with an area of

30000

square meters, we can use value feature of our calculator. We will press

2 ND

and

TRACE .

Then we choose the first option in the list and type

X = 30000 .

Therefore, the number of species in the lake is about $15 .$

c To estimate the area of a lake that contains six species of fish, we can us the trace feature of our calculator. To do that we press

TRACE .

Then use the right and left arrow keys to move along the graph to get

y \approx 6 .

Therefore, the area of the lake is about $4096$ square meters.

d As the area of the lake increases, the number of fish species also increases. One possible reason for this situation can be the home range. In a larger lake, the weaker fishes can also have their own home range to live. Therefore, the stronger fishes cannot dominate them easily.

Subchapter links

Communicate Your Answer p.309

Monitoring Progress p.311-313

Exercises p.314-316

Exercise 69 Page 316

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