Question 295222: I asked a friend of mine who is proficient in math to help me with this well needless to say she has no idea. Any help would be greatly appreciated. I know we can only post 4 problems a day the problems I am submitting are homework for college however not graded. Our homework is optional for us to do, I chose to do it in order to learn so I am able to do the test at the end of the term. I want to make that clear so the tutors dont think I am looking to have people do my homework for me for a grade. These problems are not graded. Thanks for the help
A new farm pond was stocked with 2500 crappies in 2003. The crappie population in 2006 was found to be 4320.
a) Let t be the number of years after 2003 (in other words t = 0 corresponds to 2003). Write down the initial crappie population at t = 3.
b) Find the growth function of the form f(t) = y0 bt that gives the crappie population t years after 2003. The function you have found models _________________________.
c) Predict the crappie population in 2010.
d) In what year will the crappie population reach 13,000? Give the exact value for t and then use your calculator to approximate t to get the year.
e) Are your answers for (c) and (d) consistent with the given population data in your answer to (b)?
John
Found 2 solutions by richwmiller, dabanfield:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! Dear John,
It doesn't matter if the problems are for homework or not. It doesn't matter if you are in kindergarten or post grad. There is still a 4 problem limit and you have gone way over it for the day.
This is not a hard problem.
You set it up with the year as x and the
crappie population as y
You are given two years and two populations.
So you have two points to make a linear equation.
2003 2500
2006 4320
t=0 will be 2003
t=3 will be 2006
so we convert the points to
(0, 2500)
(3, 4320)
What will t be in 2010?
The problem wants you to use t instead of x and f(x) instead of y.
Let me know how you complete the equation and your results.
Answer by dabanfield(803)  (Show Source):
You can put this solution on YOUR website! A new farm pond was stocked with 2500 crappies in 2003. The crappie population in 2006 was found to be 4320.
a) Let t be the number of years after 2003 (in other words t = 0 corresponds to 2003). Write down the initial crappie population at t = 3.
b) Find the growth function of the form f(t) = y0 bt that gives the crappie population t years after 2003. The function you have found models _________________________.
c) Predict the crappie population in 2010.
d) In what year will the crappie population reach 13,000? Give the exact value for t and then use your calculator to approximate t to get the year.
e) Are your answers for (c) and (d) consistent with the given population data in your answer to (b)?
ASSUMIMG the population growth is LINEAR the growth function is a line that passes through points (0,2500) and (3,4320). If the growth is exponential the solution is much different.
The standard form of a line is f(t) = m*t + b where m is the slope and b is the value of f(t) where the line crosses the y axis.
Since the line passes through (0,2500) and (3,4320) the slope is:
m = (4320-2500)/(3-0)
m = 1820/3
m = 606.66
So we have y = 606.66*t + b
When t = 0, y = 2500 so substituting in the equation above we have:
2500 = 606.66*0 + b
b = 2500
The growth function then is y = 606.66*t + 2500
You can use the equation above to answer c and d:
c.) for year 2010 t = 7 so:
y = 606.66*7 + 2500
d.) 13000 = 606.66*t + 2500
solve the above for t.
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