Consider a pond that contains an initial population of 300 fish. When there are enough food, the population P of fish grows in function of time t (in years) as follows: P(t) = 300(1.05)'. The initial amount of feed ture for fish in the pond is 1000 units and 1 unit can feed 1 fish for 1 year. The quantity N of fish food decreases according to the function N(t) = 1000(0.92)' :

Question

Represented graphically the functions P(t) and N(t) in a same system of axes. Describe of what kind of function it is.
- Determine the domain and the range of these functions.
- Determine the point of intersection of these two curves. Specifies the coordinates, to the hundredth, and explain what they mean.
- Call this moment in time the “crisis point”. Represents the function y = N(t) - P(t). Explain the meaning of this function. What is the abscissa at the origin, to the nearest hundredth, of the function y = N(t) - P(t)? How is this value of t related to the crisis point? Comments on the validity of the mathematical model. tick of the function P(t) for values ​​of t greater than this abscissa a the origin. Draw the shape of the curve such that you think she should be there.

Answer 1

We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.

Answer 2

Very rude of you to think i didn't put any effort, i have been working on this question for literally a week now and still cant seem to figure it out. If you do not want to help you can leave. @ PsyDAG

Answer 3

Working on this for a week ????
First of all, get the equation right, it should be
P(t) = 300(1.05)^t and N(t) = 1000(.92)^t

The graphing should be trivial, or just use a website like
www.desmos.com/calculator
which will also show you the domain and range, as well as the intersection

Where do they intersect?
300(1.05)^t = 1000(.92)^t
.3(1.05)^t = .92^t
take log of both sides and use log rules ....
log .3 + t log 1.05 = t log .92
t log 1.05 - t log .92) = -log .3
t( log 1.05 - log .92) = -log .3
t = 9.11 years

of course, when t = 9.11 .... (I carried more decimals in my calculator)
P(9.11) = 300(1.05)^9.11 = 467.88...
N(9.11) = 1000(.92)^9.11 = 467.88... , as expected

so the abscissa is 9.11 and the ordinate is 467.88 or the point (9.11,467.88)
then P(9.11) - N(9.11) is obviously zero !!

At the end you say
"Draw the shape of the curve such that you think she should be there."

No idea what that is supposed to mean.