work problem

[franklin91]

The fish population in a certain lake rises and falls according to the formula
F = 1000(29 + 15t ? t^2).
Here F is the number of fish at time t, where t is measured in years since January 1, 2009, when the fish population was first estimated.
(a) On what date will the fish population again be the same as it was on January 1, 2009?
(b) By what date will all the fish in the lake have died?


i have no idea how to start or even go about this question......if someone could help i would appreciate it thank you so much

 

[mmm4444bot]

fish population rises and falls according to

F = 1000(29 + 15t ? t^2)

F is number of fish at time t, where t is measured in years since January 1, 2009

(a) On what date will the fish population again be the same as it was on January 1, 2009?

(b) By what date will all the fish in the lake have died?

i have no idea how to start

Since the polynomial inside the parentheses does not factor, the first step could be to apply the Distributive Property and get rid of those parentheses. This is called "simplification".

Part (a) requires you to first determine the value of F on January 1, 2009, yes? Otherwise, how would you know what future value of t to look for, such that F is again the same as it was in 2009.

Here's the key piece of given-information for finding the value of F on 01-01-2009:

"t is measured in years since January 1, 2009"

This statement tells us the units for t: years. In other words,

t = 0 on 01-01-2009

t = 1 on 01-01-2010

t = 2 on 01-01-2011

t = 3 on 01-01-2012

et cetera

What is the fish population F on 01-01-2009 ?

By the way, if you've heard of parabolas, the graph of F is an upside-down parabola, to match the rise and fall of F over time.