High school math (population & exponents)

[novawinters]

Homework Statement

7. Between 1950 and 1989, the world’s population grew by 1.85%/a.
(a) Determine the doubling time for this example.
(b) If the population in 1950 was 2.5 billion, what was it in 1989?

Homework Equations

dt = 72%/growth rate

The Attempt at a Solution

a. dt = 72%/1.85%/a = 39 a
b. 1989-1950 = 39 years
2.5 billion multiplied 1.85%^39
6.6 x 10^19

 

[ideasrule]

That's approximately correct. To do the problem rigorously, we can write:

N=N0*1.085^n
N/N0=1.085^n
2=1.085^n

and then solve for n by taking the log of both sides.