Question

using the equation: P(t)=5000sin(30(t−7))+8000

When is the population about 10 000?

Answer 1

I got 7.8 months as my first answer
but can someone confirm if there is another answer to this question

Answer 2

There are actually an infinite number of answers to this problem since the sine function is periodic. Your approximation is right, though that is actually the second answer for positive t. The first answer is actually about 0.214.

See this http://www.wolframalpha.com/input/?i=5000sin%28%28pi%2F6%29%28t%E2%88%927%29%29%2B8000%3D10000

Answer 3

so how do you get the first answer which is 0.214 ?

Answer 4

To be honest, the best way to get that answer is just to graph it. However, notice that the equation is symmetric about x=4 (meaning if you reflect everything to the left of x=4 over that line, you would get the right side). Also notice that the point I showed you is the reflection of your point over that line (your point is about 4+3.8, mine is 4-3.8). This could give you some help finding this point without a graph, but when you get down to it, sometimes a simple graph (like the link I gave you) is just the best way to solve a problem like this.