So working on a exp growth word problem. I see the function should be P(t) = P0e^kt
however they give me a function in the problem already
f(t) = 100,000/(1+5000e^-t)
so when solving should I just use the function they gave me instead of the P(t) = ?
they want initial start of population, population after 4 weeks, and how many weeks to reach 40,000
I get this for the first
1) f(t) = 100,000/(1+5000e^0) = 100,000/5001
2) f(t) = 100,000/(1+5000e^4) = correct form to put into calcualtor?
3) this is where we need to solve for t correct?
im completly lost on how to solve for t. I know 1^-x = 1/x..but will this work for e^-1 or should I just move it in front. blah :/
I was able to come up with the same number after some one . but 1.5/5000 doesn't reallly give me a time frame for the answer. Answer 1 we were given t to solve for population, same with 2. 3 we are given population and told to find time. The first was intial time. So =0. Second was after 4 weeks. So t=4. However i can't see to use this information we have to get a week time frame. Maybe im missing something really obvious..sorry :/
so I did e^-t = 1.5/5000 and changed to 1/e^t = 1/1.5/5000 = 5000/1.5 gives me around 3,333. It just dont seem like the correct answer :/