Question

the population of a city is given by 3000e^(kt), where t = 0 corresponds to the year 1960. in 1950 the population was 2400. Find k to the thousandth place, and predict the population in 2015.

Answer 1

using the point (-10,2400), we have
3000 e^(-10k) = 2400
so, k = 1/10 ln 1.25 = 0.022
Now you can use the function as needed

Answer 2

@oobleck So I assume 1/10 is 1 year, but where does ln 1.25 come in from? If I follow correctly, you should end up with 600 = e^(-10k). Correct me if I made a mistake.

Answer 3

so do it
e^0 = 1 so population was 3000 in 1960
when t = - 10, p = 2400
3000 e^-10k= 2400
e^-10 k = 24/30 = 12/15 = 0.8
ln e^-10 k = -10 k = ln 0.8 = -.223
k = .223/10 = 0.0223
so
p = 3000 e^0.0223 t
2015 - 1960 = 55 = new
so put 55 in for t

Answer 4

if e^-10k = 4/5, then e^10k = 5/4 = 1.25

Answer 5

I understand now. I was doing 2400 - 3000. Had I don't division and followed through, I would have seen it. Thank you both!

Answer 6

You are welcome.