[Math] Find exponential decay equation for tiger population model

calculusexponential function

I've forgotten how to do it first it starts..

In 1900, there were 100,000 wild tigers worldwide; in 2010 the number was 3200.

(a) Assuming that the tiger population has decreased exponentially, find a formula for f(t) , the number of wild tigers t years since 1900.

(b) Between 2000 and 2010, the number of wild tigers decreased by 40% . Is this percentage larger or smaller than the decrease in the tiger population predicted by your answer to part (a)?

For (a) I assumed 

f(t) = 100'000 *N^t 
f(110) = 100'000 *N^110 = 3200
                      N = (32/1000)^(1/110)    
                        = 0.9691....

Therefore…

f(t) = 100'000*0.9691^t

Which I know is wrong.

Best Answer

Your formula $$100000*0.9691^t$$ is actually an increasing function.

Try $$f(t)=100000\times N^{-t}$$ Spoiler:Answer:

$$f(t)=100000\times(1.0318)^{-t}$$

From the formula get no. of tigers in 2000 and 2010, then find decrease percent.

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