# Thread: Finding exponential growth rate

1. ## Finding exponential growth rate

THe population of Murrayville doubled in 30 years. What was the exponential growth rate?

2. This question is exactly similar to the last question i answered for you.

$\displaystyle n = \frac{ln2}{ln(1 + r/100)}$

where n is the doubling period

so n = 30

and r is the rate

3. Originally Posted by dc52789
THe population of Murrayville doubled in 30 years. What was the exponential growth rate?
$\displaystyle r = \frac {\ln 2}t$

where $\displaystyle r$ is the rate of growth and $\displaystyle t$ is the doubling time

(note that the same formula works for half-life)

4. Originally Posted by treetheta
This question is exactly similar to the last question i answered for you.

$\displaystyle n = \frac{ln2}{ln(1 + r/100)}$

where n is the doubling period

so n = 30

and r is the rate
where did you get 100?

5. Originally Posted by dc52789
THe population of Murrayville doubled in 30 years. What was the exponential growth rate?
An exponential function can always be written $\displaystyle y= Ae^{kx}$. The "exponential growth rate" is the constant, k.

The population when x= 0 is $\displaystyle Ae^0= A$. 30 years later, x= 30 and the population is 2A: $\displaystyle 2A= Ae^{30k}$ so [tex]e^{30k}= 2. Taking the logarithm of both sides 30k= ln(2) and k= ln(2)/30.

6. Originally Posted by dc52789
where did you get 100?
it's the formula q:

refer to:
Doubling time - Wikipedia, the free encyclopedia