Hi guys, I am just asking if there's any way I can solve the following problem with an equation (I did it the long way but it's too time consuming).

Data 1: 332 people on October 2016 increasing by 19.5% every 3 months (January 2017 --> April 2017 ---> July 2017 ---> October 2017 etc.)

Data 2: 300 people on October 2016 increasing by 25.5% every 3 months (January 2017 --> April 2017 ---> July 2017 ---> October 2017 etc.)

In what month and year does Data 2 eclipse Data 1?

Long answer I got July 2017. I tried to make it into an inequality but I got April 2018 which isn't right.

What have you been taught about exponential growth problems? If you can't remember, you should be able to work it out: Take the following problem starting at time zero with population of p

_{0} population increasing by rate r percent every t

_{0} periods. For each period we need to multiply the initial population 1+r/100. In an amount of time t, there are t/t

_{0} periods of length t

_{0}. So at the end of time t, the population P is p

_{0} multiplied by 1+r/100 t/t0 times or

P = p

_{0} (1+r/100)

^{t/t0}
For your problem, the first data set has p

_{0} = 332 r = 19.5% and t

_{0}=3 if we measure time in months starting from the beginning of Oct.

P

_{1}(t) = 332 (1.195)

^{t/3}
So what is P

_{2}(t) and at what time t does P

_{2}(t) become larger than P

_{1}(t).