a To restrict the domain press 2nd and MATH. Then, use the fourth option and sixth option in the TEST column and first option in the LOGIC column.
B
b To estimate the number of species press 2ND and TRACE. Then choose the first option in the list and type X=30 000.
C
c To estimate the area of a lake press TRACE. Then use the right and left arrow keys to move along the graph to get y≈ 6.
D
d Examine the graph you drew in Part A. Consider a possible reason for the situation.
A
aGraph:
B
b 15 species
C
c 4096 square meters
D
d See solution
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 ≤ A ≤ 35 000. 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 30 000 square meters, we can use value feature of our calculator. We will press 2ND and TRACE. Then we choose the first option in the list and type X=30 000.
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≈ 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.
