SOLUTION: Ok, one last one that I need help on. I get really stuck and frustrated on word problems and this one is overwhelming me. thxs Lauren A new farm pond was stocked with 2500 cra

Question 296092: Ok, one last one that I need help on. I get really stuck and frustrated on word problems and this one is overwhelming me. thxs Lauren
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)?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A new farm pond was stocked with 2500 crappies in 2003.
(0,2500)
----------------
The crappie population in 2006 was found to be 4320.
(3,4320)
----------------
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) = yo*b^t that gives the crappie population t years after 2003. The function you have found models
---
2500 = yo
---
4320 = 2500*b^3
1.729 = b^3
b = 1.2
----------------------
Model: f(t) = 2500*(1.2)^t
----------------------
c) Predict the crappie population in 2010.
f(10) = 2500*1.2^10
f(10) = 15479
----------------------
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.
13000 = 2500*1.2^t
5.2 = 1.2^t
t*ln(1.2) = ln(5.2)
t = [ln(5.2)/ln(1.2)]
t = 17.2995...
t is appox 17 years
==========================
e) Are your answers for (c) and (d) consistent with the given population data in your answer to (b)?
Comment: I'll leave that opinion to you.
============================================
Cheers,
Stan H.

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