Please solve this question:
I'm sorry, but the policy you saw in the "
Read Before Posting" announcement remains in effect; namely, we don't "do" students' work for them, we do not give out the answer, and we don't generally even provide much (if any) assistance until the student posts his/her efforts so far (so we can see where things are bogging down).
The population of a certain community is known to increase at a rate proportional to the number of people present at any time.
Back in algebra, you learned about variation relations (
here). If the rate of growth in the population at time t is y and the actual population at time t is P, then what equation do you get from the above-quoted relation? (Use "k" for the variation constant.)
Back in algebra, you learned that "slope" can be viewed (often in the context of word problems) as "rate of change".
From calculus, you've learned that the "slope at a point" is the "derivative". So what expression can stand for "y" in your equation above?
Separating the variables and integrating both sides, what do you obtain?
If the population has doubled in 5 years, how long will it take to triple?
Given that P(5) = 2*P(0), what is the value of the constant k?
Given this value for the constant, what do you obtain as the value for t when you plug in P(t) = 3*P(0)?
Please be complete. Thank you!
