5. Suppose the population (in thousands) of a certain species of insect after / months is described by the 100t function P(!) = 41+ + 500. Determine the maximum population in the first three months. Explain 12+400 the trend in the insects population. [/C10]Optimization - Algorithm 1. Read and understand the problems text 2. Draw a diagram (if necessary). 3. Assign variables to the quantities involved and state restrictions according to the situation. 4. Write relations between these variables. 5. Identify the variable that is minimized or maximized. This is the dependent variable 6. Use the other relations (called constraints) to express the dependent variable (the one which is minimized or maximized) as a function of one single variable (the independent variable). 7. Find extrema (maximum or minimum) for the dependant variable (using global extrema algorithm, first or second derivative test). 8. Check if extrema satisfy the conditions of the application. 9. Find the value of other variables at extrema (if necessary). 10. Write the conclusion statement