# Math Help - Using graphs to solve Equations (graphing calculator)

1. ## Using graphs to solve Equations (graphing calculator)

The average wingspan of a certain species of moth is 8 cm. The wingspan for new moths varies in a periodic manner from year to year. An equation that models the wing span is w(t) = cos^3(t) - sin(t - 3) + 8, where w(t) is the wing span in cm, and t is the time in years. A biologist monitors the moth over a 25 year period. What is the range of the wing span? (Be accurate to the nearest tenth of a cm.)

2. If you are using a graphical calculator, then I assume you can find the maximum point and minimum point of the graph by using the "solve" or similar operation on the calculator.
This is when (dy/dx) is equalled to 0, or in your case, when w'(t) = 0. Once you have your maximum and minimum, you can find the range.

Or alternately you can do a bit of calculus and work it out yourself...

$w(t) = cos^3{t} - sin{(t - 3)} + 8$

$w'(t) = ...$