# Thread: Population Growth rate formula

1. ## Population Growth rate formula

Hi,
I know how to find the population growth if a growth rate is given but how do I find the growth rate if only number of years and estimated population given.ie population now = 23600 and after 53 years will exceed 35000

Thanks...Mark

2. Originally Posted by manich44
Hi,
I know how to find the population growth if a growth rate is given but how do I find the growth rate if only number of years and estimated population given.ie population now = 23600 and after 53 years will exceed 35000

Thanks...Mark
Exponential growth is modelled by $\displaystyle A(t) = A_0e^{kt}$

Where

• $\displaystyle A(t)$ = Number at time $\displaystyle t$
• $\displaystyle A_0$ = Number at $\displaystyle t=0$
• $\displaystyle k$ = growth constant $\displaystyle k>0$
• $\displaystyle t$ = time

In your example there is enough information to find $\displaystyle k$. Rearranging the equation to make k the subject:

$\displaystyle k = \frac{1}{t}(ln[A(t)] - ln(A_0))$

The equation at the top is one you should learn as it's rarely given in exams