statistics!!!?

Question

The population of Tanzania in 1995 was about 28.5 million, with an annual growth rate of 3.0 (model: P = 28.5(1.03)^n)

Predict when the population will reach 30 million.

please explain as you're solving. thank you very much

Answer 1

When n=0 you have P=28.5. What you are looking for is the value of n when P=30

So you substitute P=30 and solve the equation for n. You will need logarithms to do this.

P=28.5(1.03)^n
30=28.5(1.03)^n
30/28.5 = 1.03^n

Take the logs of both sides

ln(30/28.5) = nln(1.03) since log(a^b) = alog(b)

n = ln(30/28.5)/ln(1.03)

plugging this into a calculator you get

n = 1.735

So the population will become 30 million late in the 2nd year.

If you want to predict a date, then assuming the population is 28.5 million on January 1, 1995 then

n=1.735 ~ October 1, 1996

what you do is multiply 0.735 by 365 days and you get 268 which is about 270 days or 9 months. Then n=1.735 means about 1 year and 9 months later which is around October 1, 1996.

Answer 2

1). 1.03^n = 30/28.5
Now take the logarithm of both sides:
2). n*log(1.03) = log(30/28.5)
3). n = log(30/28/5)/log(1.03) = 1.735 years.(approx.)