Question

The amount of trout y (in tons) caught in a lake from 1995 to 2014 can be modeled by the equation y = -0.08x2 + 1.6x + 10, where x is the number of years since 1995. When were about 15 tons of trout caught in the lake? The year and the year .

Answer 1

For this case, the first thing we want to do is substitute the value of y = 15 in the equation.
 We have then:
 15 = -0.08x ^ 2 + 1.6x + 10
 Rewriting we have:
 0 = -0.08x ^ 2 + 1.6x + 10 - 15
 0 = -0.08x ^ 2 + 1.6x - 5
 The solutions are:
 x1 = 3.876275643042054
 x2 = 16.123724356957947
 Nearest whole number:
 x1 = 4
 x2 = 16
 were about 15 tons of trout caught in the lake in the years:
 1995 + 4 = 1999
 1995 + 16 = 2011
 Answer:
 The year 1999 and the year 2011