# Thread: Log Question

1. ## Log Question

Hello people, i got this log question and it took me ages and i still can not figure it out, can anyone explain this to me?

Q: The population of Cda is 30 m and is growing at an annual rate of 1.4%
The population of Ger is 80 m and is decreasing at an annual rate of 1.7%
In how how many years will the population of Cda be equal to the population of Ger?
(use log to solve the resulting equation and to 2 decimal places)

The answer is 31.59 yrs but i have no idea how to do it, any ideas?

2. Originally Posted by rudyzhou2
Hello people, i got this log question and it took me ages and i still can not figure it out, can anyone explain this to me?

Q: The population of Cda is 30 m and is growing at an annual rate of 1.4%
The population of Ger is 80 m and is decreasing at an annual rate of 1.7%
In how how many years will the population of Cda be equal to the population of Ger?
(use log to solve the resulting equation and to 2 decimal places)

The answer is 31.59 yrs but i have no idea how to do it, any ideas?
use the exponential growth/decay formulas.

For Cda: $P_1(t) = 30e^{0.014t}$

where $P_1(t)$ is the population (in millions) at time t since the population was 30mill

For Ger: $P_2 = 80e^{-0.017t}$

where $P_2(t)$ is the population (in millions) at time t since the population was 80mill

we want to solve $P_1(t) = P_2(t)$ for $t$

do you think you can continue?

3. oh god i see now it's natural -0.017, i did it for 0.017 lol thank you very much!