<span>1) Number of fish in the pond: y Number of years: x
</span>A pond had an initial population of 120 fish. Then when x=0, y=120. The graph must begin at point (x,y)=(0,120). Only the graph above at right and below at left begin in this point (0,120).
<span>The number of fish is exponentially decreasing by one-fourth each year. Then the first year the number of fish must decrease 120*(1/4)=120/4=30, and the number of fish after the first year must be: </span>120-30=90=120(1-1/4)=120(4-1)/4=120(3/4). Then when x=1, y=90. The point is (x,y)=(1,90) In the graph above at right when x=1, y is between 24 and 36. y=90 is not in this interval. then this graph is not the correct. In the graph below at left when x=1, y is between 84 and 96. y=90 is in this inverval. Then this is the correct graph.
Answer: T<span>he graph of the solution set for this situation is the graph below at left.
2) The equation has the form: y=y0(r)^x Where y0 is the initial population and r is the rate of reduction. In this case: y0=120 and r=1-1/4=(4-1)/4→r=3/4 Then the equation modeled by the graph is: y=120(3/4)^x
Answer: The equation modeled by the graph is that above at right: y=120(3/4)^x</span>
