what am i doing wrong?

Question

"the population of an endagered animal species is
f(x)=490(0.88)^t.
where 490 is the number of animals currently inthe population and t is the time in years. the population is decreasing at an annual rate of 12%.

so, i know the answer is 259 and i used the formula of 490e^rt but i ended up getting 268. what am i doing wrong?

Also, another equation..-7-6i, how do i figure that one out? I got as far as getting i=the square root of -1

Answer 1

One question at a time, please!
I assume you are trying to solve for t, when you know the formula and the value of f(x).
259 = 490* 0.88^t
259 / 490 = 0.88^t
0.52857 = 0.88^t
ln(0.52857) = ln(0.88^t) = t * ln(0.88) = t * (-0.12783)
-0.63578 = t * (-0.12783)
(-0.63578) / (-0.12783) = t
4.98757 = t

So the answer is about 4.99 years. At this point there is one animal dieing every 11 days, so there's not much purpose in figuring the answer to more than 2 decimal places.
(And a formula like that is an approximation to the *real* rate that the animals die, anyway.)

Answer 2

For the first question try using the formula you are given in the question: f(t) = 490 (0.88)^t. Substitute in t = 5 and you'll get 259 as the population after 5 years. There is no need to create a new formula. (For the reasons that stmc has given above.)

Assuming you are talking about a complex number, then -7-6i is -7-6i. There is nothing to figure out. Is there something specific that you were asked to do with that number?

Answer 3

As for the endangered animal problem, I suspect that you have been asked to find the population after 5 years. Please read your problem to see if "5 years" is mentioned somewhere.

If you have been asked to find the population after 5 years, replace the "t" in "490(.88)^t" with 5, and simplify--don't change forms to 490e^rt.

If you have been asked when the population will be 259, I would set 490(.88)^t = 259, divide both sides by 490, and use logs to finish it.
t * log(.88) = log(259/490)
t = [log(259/490)]/[log(.88)]

If it was something else, please clarify the question.


Your second problem, -7-6i, isn't an equation. What are you being asked to do?

Answer 4

In this problem, the population decreases 12% ONCE a year, not CONTINUOUSLY decreases 12%.

If you use A=Pe^(rt), that means the population decreases 12% hourly or every minute or even every second.