SOLUTION: Hoe do I go by obtaining the equation using the format in parentheses? A particular species of rare jungle bird is in danger of extinction. Fifteen years ago, the population

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Question 713839: Hoe do I go by obtaining the equation using the format in parentheses?

A particular species of rare jungle bird is in danger of extinction. Fifteen years ago, the population was 18,500 and has been decreasing exponentially (A = A0ekt). Today only 5,600 of the reptiles are alive.
a. Identify the exponential growth equation that models the population over time.
b. Using this equation, how many birds would we expect to be alive twenty years from now?

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Using time 0 as 15 years ago, A%5B0%5D=18500, and A=5600. Use these to find k.

5600=18500%2Ae%5E%28k%2A15%29
%2856%2F185%29=e%5E%28k%2A15%29
ln%2856%2F185%29=k%2A15%2A1
k=%281%2F15%29ln%2856%2F185%29
highlight%28k=-0.0797%29

a. The decay equation to model the exponential DECAY (not growth) is A=A[0]e^(-0.0797t). You choice of A[0] depends on when you want to take time point for zero time. You can choose "now" as time=0, and then A%5B0%5D=5600. For now, current time decay equation, then you can say highlight%28A=5600%2Ae%5E%28-0.0797t%29%29.

b. For twenty years from now, to find how many birds living, (a prediction), use t=20. Compute A. Use the equation that was just found.