# Word problem re: bird species extinction

#### trip20

##### New member
Here's the word problem

"A bird species in danger of extinction has a population that is decreasing exponentially (A=A_0 e^kt). Five years ago the population was at 1400 and today only 1000 of the birds are alive. Once the population drops below 100, the situation will be irreversable. When will this happen?"

I'm not sure if I formatted the equation correctly so just to be clear it's:

A = A (subscript zero) e (superscript kt)

I'm not even sure where to start? Any assistance would be greatly appreciated.

Thank you

#### galactus

##### Super Moderator
Staff member
I don't believe this is a beginner's algebra problem.

You can find k first, then use that to find the time until the population drops to 100.

$$\displaystyle \L\\1000=1400e^{k(5)}$$

Solve for k.

Once you have k, use it in the equation to find t:

$$\displaystyle \L\\100=1400e^{kt}$$

Solve for t.