The population in a town of 40,000 is growing by 12% per year. How long will it take the population to grow to 230,000? Round to the nearest year.
suppressing all the useless zeroes, we have
4*1.12^t = 23
t = 15.43
To determine how long it will take for the population to grow to 230,000, we can use the formula for exponential growth:
Population = Initial Population × (1 + Growth Rate/100)^Time
In this case, the initial population is 40,000, the growth rate is 12%, and the target population is 230,000. We need to solve for time.
Let's set up the equation:
230,000 = 40,000 × (1 + 12/100)^Time
Simplifying further:
5.75 = (1.12)^Time
To solve for Time, we can take the logarithm of both sides of the equation:
log(5.75) = log((1.12)^Time)
Using the logarithmic property (log(a^b) = b × log(a)):
log(5.75) = Time × log(1.12)
Now we can solve for Time by dividing both sides by log(1.12):
Time = log(5.75) / log(1.12)
Using a calculator, we find:
Time ≈ 12.46
Rounding to the nearest year, it will take approximately 12 years for the population to grow to 230,000.