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.

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